wkdjrk mÍlaik diagnostic testsnie.lk/pdffiles/other/som measurmaths.pdf^ introduction to...

.Ks;h

wkdjrK mÍlaIK

DIAGNOSTIC TESTS

ñkqï

.Ks; fomd¾;fïka;=júoHd yd ;dlaIK mSGh

cd;sl wOHdmk wdh;khY%S ,xldj

II

b.ekaùu iy bf.k .ekSu

;u mdif,a whym;a ld¾hidOkhla fmkakqï lrk isiqkaf.a bf.kqï ÿIalr;d wkdjrKhlr .ekSu i|yd .=rejrhdg wjYH jk uQ,sl lreKq fuu fmd; u`.ska iemfha' úIhud,djl%shd;aul lsÍfï § .=rejreka isys ;nd .; hq;= lreKla jkafka" Tjqkaf.a l%shdldrlï u`.skaorejkaf.a nqoaêuh idOkh iy p¾hd j¾Okh fj; iqúYd, jQ;a §¾>ld,Sk jQ;a n,mEula flfrknj h'

wOHdmkfha §" úNd.j,g uqyqK §fuka miq ;uka idOkh lr .;a M,fhys i;=g N=la;sú£ug isiqkag yels jk fia uQ,sl úIh lreKqj, wfmalaIs; m%ùK;d uÜgï ,nd .ekSu i|yd" ish¨mdi,a orejkag wjia:djla i,id §u rcfha wfmalaIdj hs'

orejdf.a p¾hd j¾Okh ms<sn| j ie,lSfï § wOHdmkfha wruqK jkafka" nqoaêuh idOkh"jev f,dalh iu`. iïnkaO lsÍu h' tneúka mdif,ka mßndysr f,dalh iu`. lghq;= lsÍugYsIHhdg wjYH jk ksmqK;d ixj¾Okh lsÍu msKsi Tjqkag úIhud,dj bÈßm;a lsÍu .=rejrhdf.ald¾hNdrh fõ' fï lafIa;%j,g jeo.;a fmdÿ ksmqK;d lsysmhla wh;a fõ'

• ld¾hCIu ld¾h iodpdrh - Okd;aul wdl,am" kfjda;amdok flfrys we;s leue;a;yd wêIaGdkYS,S j lghq;= lrf.k hdu'

• wka;¾-mqoa., iïnkaO;d - lKavdhï jev" úkh iy M,odhS ikaksfõokh

• m%cd idrO¾u - úúO;ajhg .re lsÍu jeks m%cd .=K O¾uj,ska iukaú;idOq .=K iïmkak mqoa.,fhla

wjidk jYfhka fuu bf.kqï-b.ekaùï l%ufõoh foi l<ukdlrKfhys i|yka jk 4 Aflfrys" tkï wdl,amh (Attirude), úYaf,aIKh (Analysis)" l%shdud¾.(Action)" yd j.ùu(Accountability)" flfrys wjOdkh fhduq lrk f,i mdi,aj, isák ish¨ u úÿy,am;sjrekaf.ka".=rejrekaf.ka yd fjk;a ld¾huKav,j,ska b,a,d isàug uu leue;af;ñ' wjidk m%;sM,h ms<sn|j WÑ; yd Okd;aul wdl,am iys; j Tn lrk ld¾hh wdrïN lrkak ^Tfí mdvu wdÈh&;ixúOdkh lrkq msKsi f;dr;=re fidhkak" ,nd .kak" úYaf,aIKh lrkak ̂ ieis ie,iqï wdÈh&;úl,am i,ld n,d ld¾hCIu f,i wm%ud§ l%shdud¾.hla .kak ̂ fnod .kak&; j.ùu ̂ ysñldß;ajh&iy;sl lrkq jia" ,efnk m%;sM, wëCIKh lrkak" ;lafiare lrkak" uek n,kak'

b.ekaùfuys ksr; jk ish¨ u .=rejrekag" bf.k .ekSfï yd b.ekaùfï m%S;sh ,efíjd hsm%d¾:kd lsÍug uu fuh wjia:djla lr .ksñ' fuu fmd; iïnkaOfhka jk Tfí ksÍlaIK ydw;a±lSï ms<sn| j" cd;sl wOHdmk wdh;kfhys wod< wOHhkdxYfha m%Odkshdg ^wjYH úfglug o msgm;la iys; j& ,shd tùug fkdmelsf<kak'

uydpd¾h .=Kmd, kdkdhlaldr" o¾YkY+Í ^ld,agka&

wOHlaI ckrd,a

cd;sl wOHdmk wdh;kh

III

fmrjok

.Ks; úIhud,dj u`.ska YsIHhka ;=< ixj¾Okh lsÍug wfmalaIs; yelshdj,ska oekqu yd

l=i,;dj" ikaksfõokh " iïnkaO;d oelau " fya;= oelaùu yd .eg¨ úi£u m%Odk fõ' ´kE u

wfhl=f.a idudkH Ôú;h ;=< ixj¾Okh lr.; hq;= yelshd f,i wm f.jk m%dfhda.sl Ôú;h

foi ne¨úg fuu yelshd ukdj meyeÈ,s fõ' th tfia jqj o oYl .Kkdjla ;siafia .Ks;h úIh

YsIH idOk uÜgu by< kexùu i|yd úúO l%fudamdhka Ndú; l< o YsIH idOk uÜgu 50]

m%udKhla jgd jk nj w'fmd'i ^id'fm<& m%;sM, fmkakqï lrhs' tfiau Wiia fm< yeoEÍu i|yd

o .Ks;h w;HjYH fõ '

by; lreKq foi úuis,su;aj ne,Sfï § .Ks;h úIh YsIH idOk uÜgï by< kexùu i|yd

oekg Ndú; l%fudamdhka m%udKj;a fkdjk nj cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=fõ

ye`.Suhs' fï i|yd úl,am úi÷ula f,i wkdjrK mÍlaIK ms<sn|j wjOdkh fhduq fldg we;'

.Ks; úIfha ish¨u ixl,am wjfndaOh i|yd ixl,am w;r ;sria yd isria ifudaOdkh ms<sn| j

oekSu wjYH fõ' tfukau iEu ixl,amhla u ir, nfõ isg ixlS¾K nj olajd wjfndaOh wjYH

fõ' tu ksid tla tla YsIHhd tla .Ks; ixl,amhl okakd uÜgu wjfndaO lr f.k t;eka isg

ixl,amh bf.kSug Tjqkag wjia:dj ,nd §u iEu .=rejrfhl=f.a u j.lSuls' tneúka .=rejrhdg

YsIH yelshd iy fkdyelshd fyd¢ka y\qkd .ekSug yelsjk mßÈ tla tla f;audj, wka;¾.;h

iqúfYaIs mshjr .Kkdjlg fnod we;' tu iEu mshjrl § u isiqka ,nd .; hq;= oekqï y÷kd .ekSug

iqÿiq m%Yak YsIHhkaag .e<fmk f,i ilia lr we;' fuu.ska .=rejrhdg YsIHhkaf.a yelshd iy

fkdyelshd iy tla tla YsIHhdf.a oekqu uÜgu y\qkd .ekSug yels fõ'

.=rejrhd fuu WmlrK ms<sn| j wjfndaO lr f.k YsIHhdg .e<fmk m%Yak ldKav ,nd §u

u`.ska .=rejrhdf.a ld¾hhg;a YsIHhkaag;a myiq jkq we;'

fuu WmlrKj, m%dfhda.sl nj iy j,x.= nj y÷kd .ekSug w;ayod ne,Sï o isÿ lr we;' fuu

WmlrK YsIHhkaaf.a .Ks; oekqu l%ñl j j¾Okh lsÍug WmldÍ jkq we;' fuu i;a ls%hdj

lsÍu i|yd odhl jQ cd;sl wOHdmk wdh;kfha jHdmD;s lKavdhug;a ndysr iïm;a mqoa., odhl;aj

oela jq ieug;a w;ayod ne,Sï i|yd odhl jq ieug;a tfuka u fiiq ld¾hj, § iydh jQ ieug;a

ia;=;s lrñ'

fla'wd¾'m;auisß

wOHlaI

.Ks; fomd¾;fïka;=j

IV

ye¢kaùu

.Ks;h ixl,amuh úIhla nj wOHdmk{hska f.a u;h hs' .Ks;h bf.kSfï § .Ks;uhixl,am f.dvke.Su isÿjkafka wkql%uhla" ms<sfj<la" wkqj fõ' uQ,sl ixl,am .%yKh fkdùfukamiqld,Sk j oaú;Shsl ixl,am .%yKh lr .ekSug ÿIalr fõ' bka Ydia;S%h lghq;=j, W!k idOkhlawe;s fõ' W!k idOkh fya;=fjka wOHdmkh ms<sn| j we;s wdYdj ySk ù bf.kqfuka bj;aùug ydNS;shla we;s lr .ekSug fm,fò' fuu ;;a;ajh wm rfÜ orejkaf.a .Ks; wOHdmkh yd Rcq f,iu ne£ mj;akd nj ie,lsh yels h'

wkdjrK mÍlaIK hkq fudkjd o @

YsIHhkaa ;=< ;sfnk hï hï ÿ¾j,;d wkdjrKh lr .ekSfï wruqKska meje;afjk mÍlaIKwkdjrK mÍlaIK kñka ye¢kafõ' uQ,sl l=i,;d W!k;dj b.ekaùfï jevms<sfj<la wdrïNfha §u y÷kd .ekSu wjYH h' wkdjrK mÍlaIK ilia lrkqfha fujeks W!k;d y÷kd .ekSfï woyiskah' ̂ idOk mÍlaIK - 16 msgqj& wkdjrK mÍlaIKhl ld¾hh jkqfha hï iqúfYaI wOHhk lafIa;%hlafyda úIh lreKla wdYs%;j YsIHhd fmkakqï lrk iqúfYaIs ÿ¾j,;d yd olaI;d fidhd .ekSu hs' ̂ Introduction to Educational Measurment - page 445& ́ kE u nqoaêu;a b.ekaùï ls%hdj,shl ydM,odhs ud¾f.damfoaYhl moku wkdjrKh fõ' ( Practice of Educational Measurment - page 220 )

.=rejrhdf.a m%Odk N+ñldj jkafka YsIHhkaa w;r .=Kd;aul bf.kqï ls%hdj,shla we;s lr,Su hs'

fuh l< yels jkafka YsIHhka ls%hdldÍj bf.kqï ls%hdj,shg iyNd.s jkafka kï muKs'bf.kqï,dNshd bf.kqï b.ekaùï ls%hdj,sfha § isÿlrkq ,nk jerÈ y÷kd .ekSu wjYH fõ' fuumshjf¾ § .=rejrhdf.a ld¾h ffjoHjrfhl=f.a ld¾h yd iudk h' ffjoHjrhd frda.shdf.a frda.hy\qkd .ekSu i|yd úúO mÍlaIK isÿ lr" frda.h wkdjrKh lrf.k" ta i|yd kshñ; m%;sldr,nd foa' wOHdmkfha § wkdjrK mÍlaIK o yeisfrkafka frda.h y÷kd .ekSu i|yd ffjoHjrhdfhdod .;a mÍlaIKj,g iudk whqßks'

wkdjrK mÍlaIK mka;s ldurfha flfia Ndú; lrkafka o @

kshñ; úIh tallhla fyda ud;Dldjla iïmq¾K lsÍfuka wk;=re j YsIHhkaf.a idOk uÜgu

mÍlaIKhla u.ska ;lafiare lsÍu isÿ flf¾' fuu ;lafiarefjka YsIHhka ms<sn| j hï hï

ks.ukj,g t<öug yels fõ' we;eï YsIHhkaa wfmalaIs; idOk uÜgu fmkakqï lrk w;r we;eï

YsIHhka wfmalaIs; idOk uÜgï lrd t<ö fkdue;s nj ;yjqre lr .; yels fõ' oeka fuu

wfmalaIs; idOk uÜgug <Õd ù fkdue;s fifuka bf.k .kakd YsIHhkag ta i|yd n,mE fya;=fudkjd oe hs úuid ne,sh hq;= fõ' fï i|yd úúO fya;= mej;sh yels h' úfYaIfhka u fodaIfmkakqï lr we;s ÿIalr lafIa;% yd ixl,am fidhd .ekSu w;HjYH fõ' fuf,i bf.kqï ÿIalr;dmj;akd lafIa;% y÷kdf.k Bg fya;= úksYaph lsÍu i|yd wkdjrK mÍlaIK fhdod .; hq;= fõ'

bf.kqï ÿIalr;d mj;akd lafIa;% y÷kd .ekSfuka miq j YsIHhka fyd¢ka m%;spdr fkdoelaùugfya;= fidhd .; hq;= fõ' tys § .=rejrhdf.a ld¾hNdrh frda. úksYapfha fhfok ffjoHjrfhl=f.ald¾hNdrhg iudk fõ' wOHdmk ls%hdj,sh ;=< fuu ;;a;ajh i|yd fhdod .kakd l%uh wkdjrK

mÍlaIK f,i yeÈkafõ' idudkH we.hSul § YsIHhkaf.a idOkh ;lafiare flrk ^assess) w;r"

wkdjrK mrSlaIKhl oS YsIHhkaaf.a yelshd úYaf,aIKh ( analysis ) flf¾'

wkdjrK mÍlaIKhl § my; oelafjk mshjr ms<sn| j wjOdkh l< hq;= fõ'

i Woõ wjYH YsIHfhda ljryq o @

V

ii fodaI iys; úIh lafIa;% $ ixl,am fudkjd o @iii fuu fodaI we;s ù ;sfnkafka l=ula ksid o@by; lreKq mokï lr f.k .Ks;h i|yd 6-9 fY%aKs úIh wka;¾.;hg wod<j wkdjrK

mÍlaIK lÜg, myla cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=j úiska ilia lrk ,§'wvq idOk uÜgï fmkakqï lrk bf.kqï ÿIalr;d iys; úIh laafIa;% y÷kd .ekSfuka miqjbf.kqï ÿIalr;dj,g fya;= úuid ne,Su i|yd fuu wkdjrK mÍlaIK Ndú; l< yels fõ' tlatla wkdjrK mÍlaIKh mehl muK ld,hlska ksu l< yels mßÈ ilia lr we;'

wkdjrK mrslaIK ieliSfï § wkq.ukh lrk ,o mshjr

1' m%Odk tallh jvd iqúfYaI f,i Wm tallj,g fnod .ekSu'2' iqúfYaI m%Yak fY%aKshla ,ehsia;=.; lsÍu'

tu tla tla m%Yakh tla iqúfYaI lreKla muKla mÍlaId lsÍu i|yd ilia lr we;'3' tla tla m%Yakh i|yd tl u j¾.fha ksoiqka ;=kla fyda Bg jeä ixLHdjla bÈßm;a lr

we;'thska wkdjrK mÍlaIKfha j,x.= nj by< uÜgul mj;ajd .ekSu wfmalaId flf¾'

wkdjrK mÍlaIKj, wka;¾.;h

iEu ud;Dldjla hgf;a jQ wkdjrK mÍlaIKj, my; oelafjk uq,sldx. wka;¾.; lr we;'

1' ld¾h úYaf,aIKhm%Odk tall" Wm tall yd iqúfYaI wruqKq yd tla tla wruqKg wod< m%Yak wxlhwe;=<;a lr we;'

2' wkdjrK mÍlaIK m%Yak m;%h tla m%Yak m;%hla mehl ld,hl§ wjika l< yels mßÈ ilia lr we;'3' ms<s;=re yd Wmfoia'

YsIHhka ms<s;=re iemhSfï § ms<s;=rej, wka;¾.; úh hq;= úfYaI lreKq yd uÜgïWmfoia hgf;a we;=<;a lr we;'

fuu fmdf;ys wka;¾.;h

fuu fmdf;ys wka;¾.; jkafka ixLHd hk f;audj hgf;a ieliQ wkdjrK mÍlaIK fõ'uQ,sl .Ks; l¾u hgf;a m%Yak m;% y;rla o ixLHd rgd hgf;a m%Yak m;% tlla o Nd. hgf;a m%Yakm;% ;=kla o oYu hgf;a m%Yak m;% ;=kla o" wkqmd; hgf;a m%Yak m;% ;=kla o" m%;sY; hgf;a m%Yakm;% ;=kla o" j¾.M,h hgf;a m%Yak m;% tlla o f,i wkdjrK mÍlaIK 17la fuys wvx.= fõ'

.Ks; yelshd we.hSfï § ie,lsh hq;= idOl

1' ksrjoH;dj2' m%;spdr fõ.h3' ixj¾Ok uÜgu4' .=Kd;aulNdjh

5' w;aoelSï lafIa;%h ̂ yelshd mrdih&7' Ñka;k l%uh yd ld¾h idOkh

VI

fuu wkdjrK mÍlaIK Ndú;h i|yd Wmfoia

1' wkdjrK mÍlaIKh ,nd Èh hq;= YsIHhka y÷kd .kak'

2' bf.kqï ÿIalr;d fmkakqï lrk lafIa;% y÷kd .kak'

3' wkdjrK mÍlaIK meje;aùu i|yd fhda.H fõ,djla f;dard .kak'

4' iEu m%Yak m;%hl u m<uqjk m%Yakfha isg mshjfrka mshjr W;a;r iemhSug YsIHhkaag Wmfoia

fokak'

5' fuu mÍlaIKfha jeo.;alu YsIHhkaag wjfndaO lrjkak' tu.ska W;a;r iemhSfï § idlÉPd

lsÍu fyda fldms lsÍu j<lajd .kak'

6' tla m%Yak m;%hla i|yd mehl muK ld,hla jeh fj;e hs wfmalaId flf¾'

7' YsIHhkaaf.a W;a;r m;% ,l=Kq lsÍfï § W;a;r iu. § we;s Wmfoia ms<sm¢kak'

8' hï m%Yak wxlhla hgf;a f.dkq lr we;s whs;u ish,a,g u ksjerÈ W;a;r ,nd § we;akï

muKla tu úIh lreKg wod< m%ùK;d uÜgug YsIHhd ,`.dù we;ehs i,lkak'

m%Yak m;%fha wvx.= iudka;r m%Yak ;=fkka tlla ksjerÈ kï th wyUq f,i isÿjQjla f,i

i,lkak'

9' W;a;r m;% ,l=Kq lsÍfï § .Kas; yelshd we.hSfï § ie,lsh hq;= idOl ms<sn| j ie,ls,su;a

jkak' ^ksrjoH;dj" m%;spdr fõ.h" ixj¾Ok uÜgu" .=Kd;aulNdjh" w;aoelSï lafIa;%h"

ld¾h idOkh &

10' wkdjrK mÍlaIKfhka bf.kqï ÿIalr;djg fya;= jq lreKq y÷kdf.k iqÿiq m%;sld¾h jev

ie,iqï lr ls%hd;aul lrkak'

m%;SldÍ jev ie,iqïlsÍfï § ie,lsh hq;= idOl

i. W;a;r m;% ,l=Kq lr ,l=Kq úYaf,aIKfhka YsIHhkaaf.a bf.kqï ÿIalr;d i|yd fya;=

ù we;s lreKq iqúfYaIj y÷kd .kak' tu lreKq ms<sn| j YsIHhka iu. iïuqL

idlÉPd mj;ajñka tu lreKq .eUqßka wOHhkh lrkak' yels;dla ÿrg flaj, iïuqL

idlÉPd mj;ajkak'

ii. fifuka bf.kSug fya;= jq wkshï idOl .fõIKh lrkak' m%udKj;a ;rï mqreÿ

fkdùu" mdi,a fkdmeñKSu " wikSm yd fi!LH ;;a;ajh " jerÈ mqreÿ ms<sn| ie,ls,su;a

jkak'

iii. YsIHhkaaf.a ksrjoH;dj" .=Kd;aul Ndjh ms<sn|j ie,ls,su;a ù ta ms<sn| j YsIHhkag

Wmfoia fokak'

iv. fifuka bf.k .kakd YsIHhkaaf.a fõ.h jeä lr,Su i|yd kej; kej; wNHdifha

ksr; lrjkak'

v. m%;SldÍ jev ie,iqï lsÍfï § foaYk l%uh yels;dla ÿrg neyer lrkak' lKavdhï

ls%hdldrlï" úfkdao ckl lS%vd jeks oE yels;dla ÿrg ie,iqï lrñka b.ekaùï

ls%hdj,sh fufyh jkak'

vi. YsIHhka w;r M,odhS idlÉPd yd wka;¾ ls%hd isÿ jk wdldrhg bf.kqï - b.ekaùï

ls%hdj,sh ie,eiqï lrkak'

vii. úhqla; ixl,am yels;dla ÿrg ixhqla; w;aoelSï weiqßka ;yjqre lrkak'

viii. m%;SldÍ bf.kqï ls%hdj,sh i|yd ksjerÈ yd iqÿiq bf.kqï øjH Ndú; lrkak'

ix. YsIHhkaf.a m%.;sh ms<sn| j l%udkql+, j jd¾;d ;nd .kak'

x. YsIHhkaf.a bf.kqï fodaI j<lajd Tjqka wod< úIh ks¾foaYfha úIh lreKq flfrys

fhduq lrjkak'

VII

wkdjrKh u.ska jeä ÈhqKq jQ .=Kd;aul bf.kqula fmkakqï lrkwkql%uh'

bf.kqu - b.ekaùu we.hSu YsIHhkaf.a wi;=gqodhl wkdjrKh i|yd ld¾h idOkh wjia:dj

wkdjrK mÍlaIK ÿIalr lafIa;% Woõ wjYH YsIHhka idudkH idOk mÍlaIKhlau`.ska bf.kqï msysgqjd .ekSu y÷kd .ekSu meje;aùu fyda fmr meje;aÿIalr;djg fya;= jQ mÍlaIKj, o;a;y÷kd .ekSu

by; wkql%ufha mßÈ YsIHhkaa fodaI yd ÿIalr;d fmkakqï lrk lafIa;% i|yd wkdjrK mÍlaIKf.dvkxjd YsIH yelshd úYaf,aIKh l< yels fõ' wm ilia lr we;s úIh lafIa;%hg wu;rjwfkla úIh lafIa;% w<,d wkdjrK mÍlaIK ;ekSug Wkkaÿ jkak' wm ilid we;s wkdjrKmÍlaIK ms<sn| j ixj¾Okd;aul fhdackd wm fj; okajd tjkafka kï fnfyúka lD;{ fjuq'

.Ks;h wiu;a j Wiia wOHdmk wjia:d wysñ lr .kakd ,laI ixLHd; YS% ,dxlsl orejkafjkqfjka fuu wkdjrK mÍlaIK ie,iqï lr we;' fïjd ls%hd;aul lr oefha orejkaf.a keKeiTma kexùug yelsfõjd hkak wmf.a m%d¾:kh hs '

Ô't,a' lreKdr;akfcHIaG wOHdmk{jHdmD;s lKavdhï kdhl'

m%;SldÍ jev l%shd;aul lsÍu

jeäÈhqKq jQ.=Kd;aul bf.kqu

VIII

m%;SldÍ b.ekaùumka;s ldurh ;=< isák fndfyda YsIHhka úúO bf.kqï ÿIalr;dj,ska hqla; h' ta w;r u;lfha

wvq nj" bf.kqu i|yd wNsfm%arKh ùfï ÿ¾j,;d" wjOdkh fhduq ùfï ÿ¾j,;d" .eg¨ úi§fïyelshdfõ ÿ¾j,;d" úúO ixl,am .%yKh lr .ekSfï ÿ¾j,;d iy wod< wjia:dj, § W.;a oekquksjerÈ f,i Ndú; lsÍfï ÿ¾j,;d i|yka l< yels h'

YsIHhka ;=< úúO jQ bf.kqï ÿIalr;d olakg ,efnk w;r u úúO jQ yelshd fukau úúO

bf.kqï l%u o Tjqka i;=j mj;S' iuyr YsIHhka oDYH udOHfhka bf.kSug jvd olaI w;r iuyr

wh Y%jH udOHfhka bf.kqug jvd ksmqK;ajhla olajhs' tfia u ;j;a iuyr YsIHhkaa m%dfhda.slw;aoelSï ;=,ska bf.kSug ms%h lrhs'

fï wkqj Tjqka ;=< mj;akd yelshd fuka u bf.kqï l%u o ie,ls,a,g .ksñka Tjqka ;=<mj;akd bf.kqï ÿIalr;d wju lsÍu wruqK lr .ksñka Tjqkaf.a bf.kqï mßirh ;=< Tjqkag iqÿiqksjerÈ b.ekaùfï yd bf.kqï øjH fhdod .ksñka Tjqkaf.a bf.kqfuys .=Kd;aul nj by< kexùu""m%;SldÍ b.ekaùfuka wfmalaId flf¾' m%;SldÍ bf.kqfuys wdrïNh jkafka wkdjrK mÍlaIKhlska.kakd f;dr;=re h '

YsIHhkaf.a bf.kqï ÿIalr;d wju lsÍfï wruqKska isÿ lrkakd jq m%;SldÍ b.ekaùfuys §ie,ls,su;a úh hq;= lreKq rdYshls' tajd w;r .=re iQodku " úúO bf.kqï ls%hdldrlï Ndú;h" iqÿiqbf.kqï wjia:d ixúOdkh " b.ekaùfï l%fudamdhhka" meyeÈ,s f;dr;=re iemhSu" m%Odk lreKqidrdxY .; lsÍu" bf.kqï leue;a; yd wNsfm%arKh by< kexùu" mka;s ldur ls%hdldrlï i|yd

YsIHhkaf.a ls%hdldÍ iyNd.s;ajh by< kexùu bf.kqï ls%hdj,sh flfrys wjOdrKh lsÍu iy tla

tla YsIHhkaf.a yelshd ms<sn| ie,ls,a,g .ekSu fõ'

fuu lreKq ms<sn| j iúia;rd;aulj úuid n,uq'

.=re iQodku

mdvï ms<sfh, lsÍug fmr " m%;SldÍ b.ekaùï isÿlrk .=rejrhd úiska YsIHhkaf.a bf.kqïÿIalr;d yels blaukska y÷kd.; hq;= h' ta i|yd wkdjrK mÍlaIKhla Ndú; l< hq;= fõ' thg

wkqj YsIHhdg jvd;a M,odhs b.ekaùfï ie,iqula ilia lr .; hq;= fõ' tu W.;a m%Odk lreKqjdÑl j fyda ,sÅ; j fyda mka;s ldurh fj; bÈßm;a lsÍug fhduq l< yels h' tu.ska Tyqf.au;lh ;j ÿrg;A ;yjqre l< yels fõ'

bf.kqï leue;a; iy wNsfm%arKh by< kexùu

mka;s ldur bf.kqï wjia:dj, § bf.kqï ÿIalr;d fya;=fjka l%u l%ufhka bf.kSu

i|yd Tjqkaf.a we;s leue;a; iy wdYdj wvqfõ' tneúka .=rejrhd úiska úIhud,dj" YsIHhkaf.a

wjYH;d iu. iïnkaO lr .; hq;= hs' YsIHhkaaf.a leue;a; o ie,ls,a,g .ksñka .=rejrhd úiskarij;a ls%hdldrlï ie,iqï lsÍu jvd;a M,odhS fõ'

mka;s ldur ls%hdldrlï i|yd YsIHhkaaf.a ls%hdldÍ iyNd.s;ajh by< kexùu

bf.kqï ÿIalr;d iys; YsIHfhda fndfyda úg iajhx wOHhkhl fh§ug ÿ¾j, tfia u ;rulaksyX wh fj;s' Tjqyq m%Yak weiSug fyda Tjqkaf.a woyia bÈßm;a lsÍug ue,sfj;s' tneúka .=rejrhd

tu YsIHhkaa ls%hdldÍ iyNd.s;ajh i|yd ffO¾hu;a l< hq;= fõ'

IX

bf.kqï ls%hdj,sh flfrys wjOdrKh lsÍu

b.ekaùu" oekqu iïfm%aIKh lsÍu i|yd muKla wjOdrKh lsÍu iqÿiq fkdfõ' bf.kqï ls%hdj,sh

u.ska YsIHhkag M,odhs ld¾hhla isÿ jkafka oe hs fidhd ne,sh hq;= fõ' tfia u YsIHhka úiskaTjqka W.;a foa ms<sn| is;Sug iy m%dfhda.slj w;ayod ne,Sug;a" .eg¨ úi§u i|yd;a wjia:d WodlrÈh hq;= fõ' tfiau .=rejrhd úiska tu wjia:d mßiaifuka ksrSlaIKh l< hq;= w;r Tjqkaf.al=i,;d wkqj Tjqkag wjYH iyfhda.h iy m%;sfmdaIKh ,nd Èh hq;= h' tu.ska Tjqka ffO¾hu;al< hq;= fõ'

úúO bf.kqï ls%hdldrlï Ndú;h

YsIHhka ;=< úúO bf.kqï ,laIK fmkakqï lrk neúka .=rejrhd úiska úúO bf.kqï ls%hdldrlïixúOdkh lr .; hq;= fõ' fï wkqj Tjqka ;=< mj;akd úúO yelshd yd l=i,;d fuu.ska ixj¾Okhl< yels fõ' fuys§ jvd;a M,odhs jkafka tla §¾> ls%hdldrlula ixúOdkh lsÍu fkdj wod< ir,

ls%hdldrlï fY%aKshla uÕska YsIHhkag wjYH oekqu yd l=i,;d ,nd §u hs'

iqÿiq bf.kqï wjia:d ixúOdkh

m%;SldÍ b.ekaùfuys fhfok .=rejrhd úiska iqÿiq bf.kqï wjia:d ixúOdkh lr .; hq;= h'ksoiqkla f,i bx.S%is NdIdj i|yd NdId mßirhla f.dvke.Su fyda .Ks;h úIh i|yd l%SvdixúOdkh i|yka l< yels h'

b.ekaùfï l%fudamdhhka

.=rejrhd úiska úhqla; ixl,am meyeÈ,s lsÍfï §" YsIHhkaf.a bf.kqï yelshd wkqj ixhqla;

WodyrK Ndú; lrñka ir, mshjr Tiafia th isÿ l< hq;= h' .=rejrhd úiska YsIHhkaf.a ls%hdldÍiyNd.s;ajh we;s lsÍu i|yd wjYH ;rï bf.kqï wdOdrl Ndú;h yd l%Svd iy ls%hdldrlï Ndú;dlsÍu jeo.;a h' tfiau m%Odk lreKq meyeÈ,s lsÍfï § f;dr;=re ;dlaIKh iy Ndú; l< yels ish¿

iïm;a Ndú;fhka YsIHhkag myiqfjka lreKq wjOdrKh l< yels fõ'

meyeÈ,s f;dr;=re iemhSu

bf.kqï ÿIalr;d iys; fndfyda YsIHhkaf.a ,sÅ; NdIdj wjfndaO lr .ekSfï l=i,;dj wju

uÜgul mj;S' tneúka .=rejrhd úiska ir, iy meyeÈ,s f;dr;=re iemhSfuka YsIHhkaf.a jerÈjgyd .ekSï u.yrjd .; yels h' tfiau bf.kqï ls%hdldrlï ys mshjr ir, j meyeÈ,s l< hq;= fõ'

yelskï YsIH wjYH;dj u; tu ls%hdldrlï ys mshjr kej; kej;;a meyeÈ,s lsÍu jvd;a M,odhsfõ'

m%Odk lreKq idrdxY .; lsÍu

mdvu wjidkfha .=rejrhd úiska tu mdvug wod< m%Odk lreKq kej; isysm;a l< hq;= w;r tulreKq l¿,E,a, u; i|yka l< hq;= fõ' tu.ska " Y%jH yd oDIH udOH u.ska W.;a úIh lreKqkej; isysm;a l< yels fõ' tfia u tÈfkod Ôú; w;aoelSï iu. W.;a úIh lreKq iïnkaO lr

.ekSu i|yd YsIHhka fhduq l< hq;= fõ '

Ô' mS' tÉ' c.;a l=udrfcHIaG lÓldpd¾hcd;sl wOHdmk wdh;kh

X

WmfoaYkh (uydpd¾h .=Kmd, kdkdhlaldrwOHlaI ckrd,acd;sl wOHdmk wdh;kh

tï¡ t*a¡ tia¡ mS¡ chj¾OkksfhdacH wOHlaI ckrd,aúoHd yd ;dlaIK mSGhcd;sl wOHdmk wdh;kh

wëlaIKh(fla¡ rxð;a m;auisßwOHlaI.Ks; fomd¾;fïka;=jcd;sl wOHdmk wdh;kh

ie,iqu yd iïnkaëlrKh(Ô¡ t,a¡ lreKdr;akfcHIaG wOHdmk{wOHdmk fmdÿ iy;sl m;%^id'fm<& m%;sM, by< kxjd,Sfï jHdmD;sfha lKavdhï kdhl'cd;sl wOHdmk wdh;kh

fou< udOHh iïnkaëlrKh(tia' rdfÊkaøï uhdlÓldpd¾hcd;sl wOHdmk wdh;kh

6 - 9 fY%aKs úIh wka;¾.;hg wod< j ilia lr we;'

XI

ndysr iïm;a odhl;ajh (

tÉ'tï'ta'chfiak uhd úY%dñl .=re WmfoaYl

jhs'ù'wd¾'ú;dru uhd .=re WmfoaYll,dm wOHdmk ld¾hd,h" foyss´úg

tka'Ô'fifkúr;ak uhd .=re WmfoaYll,dm wOHdmk ld¾hd,h" foyss´úg

chïm;a f,dl=uqo,s uhd .=re fiajhckdêm;s úoHd,h" uyr.u

Ô'tÉ'tia'rxckS o is,ajd ñh .=re fiajhO¾umd, úoHd,h" mkaksmsáh

ã't,a' ngq.yf.a uhd úY%dñl mSGdêm;sishkE cd;sl wOHdmk úoHdmSGh" fõhkaf.dv

mß.Kl msgq ieliqu( wd¾'mS'ã'iS' chisxy uhd.=re WmfoaYll,dm wOHdmk ld¾hd,h" foyss´úg

NdIdj ixialrKh ( tÉ¡ mS¡ iqis,a issßfiak uhdlÓldpd¾hydmsá.u cd;sl wOHdmk úoHdmSGh

msg ljr ks¾udKh ( cd;sl wOHdmk wdh;kh

iydh ld¾h uKav,h ( tia' fyÜáwdrÉÑ".Ks; fomd¾;fïka;=j"cd;sl wOHdmk wdh;kh'

fla' fk,sld fiakdks".Ks; fomd¾;fïka;=j"cd;sl wOHdmk wdh;kh'

wd¾' tï' rEmisxy".Ks; fomd¾;fïka;=j"cd;sl wOHdmk wdh;kh'

XII

mgqk

msgqj1' mßñ;sh - i

1'1' ld¾h úYaf,aIKh i 011'2 wkdjrK mÍlaIK m;%h i 031'3 W;a;r yd Wmfoia i 09

2' mßñ;sh - ii

2'1 ld¾h úYaf,aIKh ii 102'2 wkdjrK mÍlaIK m;%h ii 132'3 W;a;r yd Wmfoia ii 21

3' j¾.M,h - i

3'1 ld¾h úYaf,aIKh i 223'2 wkdjrK mÍlaIK m;%h i 243'3 W;a;r yd Wmfoia i 31

4' j¾.M,h - ii

4'1 ld¾h úYaf,aIKh ii 344'2 wkdjrK mÍlaIK m;%h ii 374'3 W;a;r yd Wmfoia ii 46

5' mßudj

5'1 ld¾h úYaf,aIKh 485'2 wkdjrK mÍlaIK m;%h 515'3 W;a;r yd Wmfoia 62

6' jD;a;hl j¾.M,h

6'1 ld¾h úYaf,aIKh 656'2 wkdjrK mÍlaIK m;%h 676'3 W;a;r yd Wmfoia 74

.Ks; fomd¾;fïka;=j cd;sl wOHdmk wdh;kh1

wkdjrK mÍlaIK ñkqï

mßñ;sh - I

ld¾h úYaf,aIKh

1'1 È. ms<sn| ixl,amh

1'2 È. uksk tall'



1' mßñ;shwkdjrK mÍlaIKh -

iúia;rd;aul ld¾h úYaf,aIKh

m%Yak wruqKq wruqKqwxlh wxlh

1'1 È. ms<sn| ixl,amh

1 1'1'1 § we;s rEm w;=ßka Èf.ka jeä rEmh f;darhs'2' 1'1'2 § we;s rEmhl kï lrk ,o m<, È.la f,i y÷kd .kshs'3' 1'1'3 § we;s rEmhl kï lrk ,o Wi È.la f,i y÷kd .kshs'4' 1'1'4 § we;s rEmhl olajd we;s .eUqr È.la f,i y÷kd .kshs'5' 1'1'5 rEmhl olajd we;s >klu È.la f,i y÷kd .kshs'6' 1'1'6 m<, " Wi " .eUqr " >klu hkq È.la f,i y÷kd .kshs'

1'2 È. uksk tall

7"8 1'2'1 È. uksk tall y÷kd .kshs'9 1'2'2 ñ,sógrj,ska § we;s È. m%udK folla tl;= lrhs'10 1'2'3 ñ,sógrj,ska § we;s È. m%udK folla wvq lrhs'11 1'2'4 fikaáógrj,ska § we;s È. m%udK folla tl;= lrhs'12 1'2'5 fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'13 1'2'6 fikaáógrj,ska § we;s È. m%udKhka ñ,sógrj,ska olajhs'14 1'2'7 ñ,sógrj,ska § we;s È. m%udKhka fikaásógrj,ska olajhs'15 1'2'8 fikaáógr yd ñ,sógrj,ska § we;s È. m%udK folla tl;= lrhs'16 1'2'9 ñ,sógr yd fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'17 1'2'10 ógrj,ska § we;s we;s È. m%udK folla tl;= lrhs'18 1'2'11 ógrj,ska § we;s we;s È. m%udK folla wvq lrhs'19 1'2'12 ógrj,ska § we;s È. m%udK fikaá ógr njg mßj¾;kh lrhs'20 1'2'13 oYu ia:dk 1 la iys; j ógrj,ska ±lafjk È. m%udKhka"

fikaáógrj,g mßj¾;kh lrhs'21 1'2'14 oYu ia:dk 2 la iys; j ógrj,ska ±lafjk È. m%udKhka"

fikaáógrj,g mßj¾;kh lrhs'22 1'2'15 W;a;r mQ¾K ixLHdjla jkfia fikaáógrj,ska ±lafjk È.

m%udKhka" ógrj,ska olajhs'23 1'2'16 W;a;r oYu ia:dk tlla jkfia fikaáógrj,ska ±lafjk È.

W;a;r oYu ia:dk folla jkfia fikaáógrj,ska ±lafjk È.m%udKhka" ógrj,ska olajhs'

25 1'2'18 ógr yd fikaásógrj,ska § we;s È. m%udK folla tl;= lrhs'26 1'2'19 ógr yd fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'

I



mßñ;sh IwkdjrK mÍlaIKh - 1

m%Yak m;%h'm%Yak ish,a,gu W;a;r imhkak'

1' my; tla tla rEm w;=ßka È.ska jeä rEmh f;dard Bg ysñ wlaIrh ysia;ek u;,shkak '

(i) (ii) (iii)

''''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''

2' w¢k ,o rEmhg wkqj § we;s m%ldYh ksjerÈ kï ,l=K o" jerÈ kï ,l=K o" Bg bÈßfhka we;s fldgqj ;=< fhdokak'

a. a.a.

b. b.b.

(i)

(ii)

(iii)

5 cm

5 cm4 cm

2 cm

4 cm

4 cm 4 cm

4 cm

2 cm

fuu RcqfldaKdi%fha hkq os.la fõ'2 cm

fuu >kldNfha hkq os.la fkdfõ'4 cm

fuu iup;=ri%fha mdohl È. fõ'4 cm



3'(i)

(ii)

(iii)

fuu rEmfhka ±lafjkafka Wi jQWux fodrls' fuys u.ska ±lafjkafka È.ls '

5 m5 m

fuu úÿ,s myka lKqfõ Wi fõ'fuu Wi" È. f,i y÷kajhs '

8 m

fuu .fia Wi ls' u`.ska ±lafjkafka È.la fkdfõ'

12 m12 m

4'

15 m

(i)

(ii)

fuu <sf|a .eUqr ógr 15 ls' fuys È.la fkdfõ '15 m

2 m

5 m

12 m

fuh la .eUqr fmdl=Kls' fuu .eUqrÈ.la f,i ±laúh yels h '

2 m

8 m



(iii)

( i )

( ii )

( iii )

1 cm

6' fmÜáhl È." m<, " Wi hk ñkqï ;=k u È. fõ'

gexlshl .eUqr È.la fkdfõ '

´kE u ;yvqjl >klu hkq È.ls '

( i )

( ii )

( iii )

fuu c,dYfha .eUqr ls ' tys hkq È.ls'3 m

3 m3 m

5.

remsh,

1 mmfuh >klula we;s ;yvqjls'tu >klu È.la f,i m%ldY l<yels h '

1 mm

,Sj,ska idod.;a yevhla fuys ±lafõ 'fuu ,S l=Üáfha >klu ls 'fuu hkq È.la fkdfõ '1 cm

1 cm

fuys ±lafjkafka remshf,a ldishls 'tys >klu jkÈ.la fkdfõ '

2 mm2 mm



7' ksjeros jrKh f;dard háka brla woskak '

k.r folla w;r ÿr uekSug iqÿiq tallh jkafka" h' h' h'

ldishl >klu uekSug iqÿiq tallh jkafka "h' h' h'

.il Wi uekSug jvd;a iqÿiq tallhla jkafka "h' h' h'

8'os. uksk tallhla fkdjkafka "

h' h' h'

Wi uksk tallhla fkdjkafka "h' h' h'

>klu uksk tallhla fkdjkafka "h' h' h'

9' tl;= lrkak '

10' wvq lrkak '

11' tl;= lrkak '

12' wvq lrkak '

13' my; tall mßj¾;kh lrkak '

( i )a ) km b ) kg c ) l

(ii )a ) m b ) mm c ) km

( iii )a ) g b ) l c ) m

(i )a ) m b ) cm c ) g

( ii )a ) mm b ) kg c ) m

( iii )a ) ml b ) mm c ) cm

( i ) 13 mm ( ii ) 24 mm ( iii ) 56 mm + 17 mm + 6 mm + 49 mm

( i ) 57 mm ( ii ) 72 mm ( iii ) 54 mm - 17 mm - 25 mm - 27 mm

( i ) 72 cm ( ii ) 54 cm ( iii ) 45 cm + 93 cm + 27 cm + 59 cm

( i ) 72 cm ( ii ) 52 cm ( iii ) 93 cm - 28 cm - 37 cm - 46 cm

( i ) 5 cm = .............mm( ii ) 7 cm = .............mm( iii ) 12 cm = .............mm



14' my; tall mßj¾;kh lrkak '

15' tl;= lrkak '

16' wvq lrkak '

17' tl;= lrkak '

18' wvq lrkak '

19' ógrj,ska § we;s È. m%udK fikaáógrj,g yrjd ,shkak '

20'

21'

22'fikaá ógrj,ska olajd we;s È. m%udK ógrj,g yrjd ,shkak'

( i ) 20 mm = .............cm( ii ) 50 mm = .............cm( iii ) 70 mm = .............cm

( i ) cm mm ( ii ) cm mm ( iii ) cm mm3 7 4 7 1 9

+ 2 5 + 2 3 + 7 5

( i ) cm mm ( ii ) cm mm ( iii ) cm mm8 2 5 3 10 5

- 1 7 - 2 4 - 7 8

( i ) 427 m ( ii ) 342 m ( iii ) 649 m + 538 m + 573 m + 249 m

( i ) 572 m ( ii ) 721 m ( iii ) 824 m - 193 m - 547 m - 172 m

( i ) 2 m = .............cm( ii ) 5 m = .............cm( iii ) 7 m = .............cm

( i ) 2.5 m = .............cm( ii ) 3.7 m = .............cm( iii ) 4.1 m = .............cm

( i ) 3.75 m = .............cm( ii ) 1.24 m = .............cm( iii ) 3.25 m = .............cm

( i ) 300 cm = .............m( ii ) 800 cm = .............m( iii ) 500 cm = .............m



23'

24'

25'tl;= lrkak'

26'wvq lrkak '



( i ) m cm ( ii ) m cm ( iii ) m cm5 24 7 45 3 77

+ 2 95 + 2 57 + 2 88

( i ) m cm ( ii ) m cm ( iii ) m cm7 45 12 25 10 55

- 3 24 - 9 70 - 4 70



wkdjrK mÍlaIKh - 1W;a;r yd Wmfoia

m%Yak W;a;r Wmfoiawxlh

1. ( i ) a ( ii ) b ( iii ) b2. ( i ) ( ii ) ( iii )3. ( i ) ( ii ) ( iii )4. ( i ) ( ii ) ( iii )5. ( i ) ( ii ) ( iii )6. ( i ) ( ii ) ( iii )

( i ) km ( ii ) mm ( iii ) m( i ) g ( ii ) kg ( iii ) ml( i ) 30 mm ( ii ) 30 mm ( iii ) 105 mm( i ) 40 mm ( ii ) 47 mm ( iii ) 27 mm( i ) 165 cm( ii ) 81 cm ( iii ) 104 cm( i ) 44 cm ( ii ) 15 cm ( iii ) 47 cm( i ) 50 ( ii ) 70 ( iii ) 120( i ) 2 ( ii ) 5 ( iii )7( i ) 6 2 ( ii ) 7 0 ( iii ) 9 4( i ) 6 5 ( ii ) 2 9 ( iii ) 2 7( i ) 965 m ( ii ) 915 m ( iii ) 898 m

18. ( i ) 379 m ( ii ) 174 m ( iii ) 652 m19. ( i ) 200 ( ii ) 500 ( iii ) 70020. ( i ) 250 ( ii ) 370 ( iii ) 41021. ( i ) 375 ( ii ) 124 ( iii ) 32522. ( i ) 3 ( ii ) 8 ( iii ) 523. ( i ) 8.7 ( ii ) 5.4 ( iii ) 3.224. ( i ) 3.75 ( ii ) 5.84 ( iii ) 7.2725. ( i ) 8 19 ( ii ) 10 02( iii ) 6 6526. ( i ) 4 21 ( ii ) 2 55 ( iii ) 5 85

7.8.9.10.11.12.13.14.15.16.17.

tall ,shd ;sìh hq;= hs'

tall ,shd ;sìh hq;= hs'



mßñ;sh - II

ld¾h úYaf,aIKh

1'3 ir, ;, rEmj, mßñ;sh'

1'4 ixhqla; ;, rEmj, mßñ;sh'

1'5 jD;a;hl mßêh



mßñ;sh IIwkdjrK mÍlaIKh



1'3 ;, rEmj, mßñ;sh1"2 1'3'1 mßñ;sh hk ixl,amh y÷kd. kshs'3 1'3'2 mdo u; È. ,l=Kq l< ;%sfldaKhl mßñ;sh fidhhs'4 1'3'3 tla mdohl È. ,l=Kq lr we;s iumdo ;%sfldaKhl mßñ;sh

fidhhs'5 1'3'4 mdoj, os. ,l=Kq lr we;ss iuoaùmdo ;%sfldaKhl mßñ;sh fidhhs'6"7"8"9 1'3'5 ;%sfldaKhl mdoj, os. ùÔh ixfla;j,ska § we;s úg tys mßñ;sh

ùÔh m%ldYkhlska olajhs '10 1'3'6 iumdo ;%sfldaKhl mßñ;sh ÿka úg mdohl È. fidhhs'11"12 1'3'7 iuoaùmdo ;%sfldaKhl mßñ;sh yd tla mdohla ÿka úg wfkla

mdoj, È. fidhhs '13 1'3'8 iup;=ri%hl ish¨u mdoj, È. ,l=Kq lr we;s úg tys mßñ;sh

fidhhs '14 1'3'9 iup;=ri%hl tla mdohl È. ,l=Kq lr we;s úg tuiup;=ri%fha

mßñ;sh fidhhs '15"16 1'3'10 iup;=ri%hl mdohl È. ùÔh ixfla; j,ska § we;súg tys

mßñ;sh ùÔh m%ldYkhlska olajhs'17 1'3'11 RcqfldaKdi%hl ish¨ mdoj, os. oS we;s úg tys mßñ;sh .Kkh

lrhs'18 1'3'12 RcqfldaKdi%hl noaO mdo foll È. ,l=Kq lr we;s úg tys

mßñ;sh fidhhs'19 1'3'13 mdoj, È. ùÔh ixfla;j,ska § we;súg RcqfldaKdi%fha

mßñ;sh i|yd m%ldYkhla f.dvk.hs'20 1'3'14 RcqfldaKdi%hl mßñ;sh yd È. ÿka úg m<, fidhhs'21 1'3'15 RcqfldaKdi%hl mßñ;sh yd m<, ÿka úg È. fidhhs'

1'4 ixhqla; ;, rEmhl mßñ;sh22"23"24 1'4'1 § we;s ;, rEm w;ßka ixhqla; ;, rEm f;darhs'25 1'4'2 ixhqla; ;, rEmhl ,laIK y÷kd .kshs'26 1'4'3 ixhqla; ;, rEmhl mßñ;sh fidhhs'27 1'4'4 ixhqla; ;, rEmfha mdo lSmhl È. yd wfkla mdoj, iïnkaO;d

,l=Kq lr § we;s úg rEmfha mßñ;sh fidhhs'28 1'4'5 ixhqla; ;, rEmhl mdoj, È. ùÔh ixfla;j,ska § we;s úg

mßñ;sh i|yd ùÔh m%ldYkhla f.dvk.hs'29 1'4'6 ixhqla; ;, rEmhl mßñ;sh .Kkh lrhs '




1'5 jD;a;hl mßêh30 1'5'1 jD;a;hl mßêh y÷kd .kshs'31 1'5'2 jD;a;hl wrh kï lrhs '32 1'5'3 jD;a;hl mßêh fiùu hgf;a ,efnk ixfla; y÷kd .kshs'33 1'5'4 jD;a; ksh;fha wdikak w.h y÷kd .kshs'34 1'5'5 jD;a;hl wrh ÿka úg mßêh .Kkh lrhs'35 1'5'6 jD;a;hl úIalïNh ÿka úg mßêh .Kkh lrhs'



fuys ±lafjkafka bvul o<rEmhls' tys jfÜ È. uek .;aúgth tu bvfï mßñ;sh fõ'

( i )

( ii )

( iii )

( i )

( ii )

( iii )

( i )

....................... ...................... .....................

bvu

<ufhla fuu f.dvke.s,af,ajfÜ È. uek Tyqg ,enqK È.mßñ;shla fkdjk nj mjihs '

<ufhla fïi ,E,af,a jfÜ È.uek.kS' ,enqKq uq¿ È.mßñ;sh f,i lshhs'

5 cm7 cm

5 cm5 cm

5 cm5 cm 3 cm

4 cm

5 cm

mßñ;sh IIwkdjrK mÍlaIKh

m%Yak m;%h

1' w¢k ,o rEmhg wkqj § we;s m%ldYh ksjerÈ kï ,l=K o" jerÈ kï,l=K o " Bg bÈßfhka we;s fldgqj ;=< fhdokak'

2' ksjerÈ jrKh f;dard háka brla w¢kak'´kEu ;, rEmhl jfÜ È. "^ j¾.M,h fõ' $ mßñ;sh fõ' $ mßudj fõ' &

fuu RcqfldaKdi% wdia;rfha mßñ;sh hkq" tys^ fl,ska È.hs' $ jfÜ È.hs' $ yria È.hs ' &

fuu ;%sfldaKdldr wdia;rfha udhsfï È. "^ j¾.M,h fõ' $ mßudj fõ' $mßñ;sh fõ' &

3' my; olajd we;s ;%sfldaKj, " § we;s ñkqï wkqj mßñ;sh fidhkak'



( ii ) (iii) ( iii )

4 cm

5 cm

10 cm

.................... ..................... ..................


..................... ..................... ..................


a a

a

p

p

p

m m

m

.................... ..................... ..................


a b

c

q p

r

m n

q

..................... ..................... .....................( ii ) (iii) ( iii )

a

p

r

.......................... ........................ ...........................

4'

5'

6'

7'

8'

5 cm

3 cm

4 cm

6 cm

10 cm5 cm



( i ) ( ii ) ( iii )

b a p m

c

..................... ..................... ..................

( i ) ( ii ) ( iii )

= 18 cm = 12 cm = 30 cm = ........... = .......... = ..........

( i ) ( ii ) ( iii )

= 18 cm = 10 cm = 32 cmx = ....... x = ........ x = .......

( i ) ( ii) ( iii )

= 40 cm = 50 cm = 30 cmx = ....... x = ........ x = .......

9'

10' my; olajd we;s iumdo ;%sfldaKj, mrsñ;sh oS we;' tajdfha tla tla mdohl os.fidhkak'

mrsñ;sh mßñ;sh mrsñ;sh mdohl os. mdohl os. mdohl os.

11' my; olajd we;s iuoaùmdo ;%sfldaKj, mrsñ;sh oS we;' tajdfha tla tla mdohl x u.ska oelafjk os. fidhkak'

mrsñ;sh mßñ;sh mrsñ;sh

12'

mrsñ;sh mßñ;sh mrsñ;sh

3 cm5 cm

x

5 cm

x

3 cm

x

10 cm 10 cm

x x x

8 cm10 cm 20 cm

r



( i ) ( ii ) ( iii )

( i ) ( ii ) ( iii )

4 cm 10 cm 6 cm

( i ) ( ii ) ( iii )

( i ) ( ii ) ( iii )

r t x

( i ) ( ii ) ( iii )

13' my; olajd we;s iup;=ri%j, § we;s ñkqï wkqj mßñ;sh fidhkak'

mßñ;sh - ''''''''''''''''''' mßñ;sh - '''''''''''''''''''''' mßñ;sh - '''''''''''''''''''''''14'

mßñ;sh - ''''''''''''''' mßñ;sh - ''''''''''''''' mßñ;sh - '''''''''''''''

15'


16'


17' my; olajd we;s RcqfldaKdi%j, § we;s ñkqï wkqj mßñ;sh fidhkak '


4 cm 5 cm

2 cm

2 cm

2 cm2 cm

4 cm

4 cm 4 cm

5 cm

5 cm5 cm

a b

aa

a

b b

b

m

mm

m

2 cm2 cm 4 cm 4 cm

5 cm

5 cm

6 cm

6 cm

3 cm 3 cm

7 cm

7 cm



( i ) ( ii ) ( iii )

( i ) ( ii ) ( iii )

( i ) ( ii ) ( iii )

= 24 cm = 50 cm = 36 cm= 8 cm = 15 cm = 10 cm= .......... = .......... = .......

( i ) ( ii ) ( iii )

= 20 cm = 30 cm = 40 cm= 4 cm = 5 cm = 5 cm= .......... = .......... = .......

18'

5 cm

2 cm

3cm

8 cm 10 cm

5 cm


19'

mßñ;sh - ''''''''''''''''''' mßñ;sh - '''''''''''''''''''' mßñ;sh - '''''''''''''''''''

20'my; RcqfldaKdi%j, mßñ;sh yd È. § we;' tajdfha m<, fidhkak'

mßñ;sh mßñ;sh mßñ;shÈ. È. È.m<, m<, m<,

21' my; RcqfldaKdi%j, mßñ;sh yd m<, § we;' tajdfha È. fidhkak'

mßñ;sh mßñ;sh mßñ;shm<, m<, m<,È. È. È.

a

b

a

ab

m

n

m

n

b



22' § we;s rEm w;=ßka ixhqla; ;, rEm f;dard " tu rEmj,g háka brla w¢kak'

23'

24' § we;s rEm lÜg, w;=ßka ixhqla; ;, rEm lÜg,h f;dard háka brla w¢kak'

25' ksjerÈ ms<s;=r f;dard háka brla w¢kak'ixhqla; ;, rEmhlg wjYH jkafka "yev;, tlla muKs' $ yev;, lSmhls '

ixhqla; ;, rEmhlg yev;, "tllaj;a wjYH fkdfõ' $ tllg jvd ;sìh hq;= hs'

ixhqla; ;, rEmhla kï tys yev;,"tlsfklg iïnkaO úh hq;= h' $ fjka fjka j ;sìh hq;= h'

26' my; olajd we;s ixhqla; ;, rEm j, § we;s ñkqï wkqj mßñ;sh fidhd ;s;a bru; ,shkak' ish¿ ñkqï olajd we;af;a fikaáógr j,sks'

'''''''''''''''''''''''''' ''''''''''''''''''''''' ''''''''''''''''''''''

( i )

( ii )

( iii )

( i )

( ii )

( iii )

( i ) ( ii ) ( iii )

3

2

5 55

5

55

33 3

2 2

4

10

6

6

2



27'

''''''''''''''''''''''' ''''''''''''''''''''''' '''''''''''''''''''''''

28'

'''''''''''''''''''''' '''''''''''''''''''''' '''''''''''''''''''''''''

29' § we;s W;a;rh w;ßka rEmfha mßñ;sh ±lafjk W;a;rh háka brla w¢kak'

30' my; m%ldYk yß o $ jerÈ o hkak f;dard ksjerÈ W;a;rh háka brla w¢kak 'jD;a;dldr fmdl=Kl jfÜ È. hkq tys mßñ;sh hs ' jD;a;fha mßñ;sh

tys mßêh kñka y÷kajhs' ^ yß $ jerÈ &

jD;a;dldr ldishl jfÜ È. tys mßêh fkdfõ' ^ yß $ jerÈ &

jD;a;hl mßêh hkq jD;a;fha mßñ;sh hs' ^ yß $ jerÈ &

31' jD;a;fha wrh l=ula ± hs fidhd wod< wlaIrh ;s;a br u; ,shkak'

''''''''''''' ''''''''''' '''''''''''''

( i ) ( ii ) ( iii )

( i ) ( ii ) ( iii )

a) 12 cm a) 26cm a) 8cmb) 24cm b) 36cm b) 12cmc) 8cm c) 22cm c) 22cm

( i )

( ii )

( iii )

( i ) ( ii ) ( iii )

d

ab

r

m

n

3

8 4

4

5 2

6 cm

2 cm

2 cm

6 cm

2 cm

4 cm 4 cm

6 cm

2 cm

10 cm

....

a

c

b

d

3a

a a

a a

b b

a

p

q

p

r

r

a

2



32' ksjerÈ W;a;rh f;dard háka brla w¢kak'jD;a;hl wrh o " úIalïNh o kï " wrh yd úIalïNh w;riïnkaOh jkafka "

jD;a;hl mßêh fidhk iïnkaOh jkafka "

j,ska ±lafjkafka

jD;a;hl wrh yd mßêh w;r iïnkaOhhs'

jD;a;hl úIalïNh yd mßêh w;r iïnkaOhhs'

33' ys w.h fidhd.kafka "mrsêh u`.sks' mßêh u`.sks'wrh úIalïNh

ys wdikak w.h jkqfha "

34' § we;s o;a; wkqj my; jD;a;j, mßêh fidhkak' ^ flakaøh fõ' &

mßêh mßêh mßêh

35'

mßêh mßêh mßêh

rc 2

7 cm14 cm

21cm

O OO

7 cm14 cm

28cm

OOO

ys wdikak w.h oYu ia:dk 2 l g ,shQúg "

O

( i ) r d

a ) d = 2 r b ) r = 2 d

( ii )

a ) b ) 2rA

( iii )a )b )

( i ) a ) b )

( ii )

a )7

22b )

22

7

( iii ) a ) 3.14 b ) 4.31

( i ) ( ii ) ( iii )

= ........ = ......... = .......

( i ) ( ii ) ( iii )

= ................. = ...................... = .......



mßñ;sh - 11wkdjrK mÍlaIKhW;a;r yd Wmfoia


1. (i) (ii) (iii)2. (i) (ii)

(iii)3. (i) 15cm (ii) 12cm (iii) 17cm4. (i) 12cm (ii) 15cm (iii) 30cm5. (i) 13cm (ii) 13cm (iii) 26cm6. (i) 3a (ii) 3p (iii) 3m7. (i) a+b+c (ii) p+q+r (iii) m+n+q8. (i) 3a (ii) 3p (iii) 3r9. (i) 2b+a (ii) 2p+r (iii) 2c+m10. (i) 6cm (ii) 4cm (iii) 10cm11. (i) 8cm (ii) 4cm (iii) 12cm12. (i) 15cm (ii) 15cm (iii) 11cm13. (i) 8cm (ii) 16cm (iii) 20cm14. (i) 16cm (ii) 40cm (iii) 24cm15. (i) 4a (ii) 4b (iii) 4m16. (i) 4r (ii) 4t (iii) 4x17. (i) 16cm (ii) 20cm (iii) 18cm18. (i) 14cm (ii) 22cm (iii) 30cm19. (i) 2a+2b (ii) 2m+2n (iii) 2a+2b20. (i) 4cm (ii) 10cm (iii) 8cm21. (i) 6cm (ii) 10cm (iii) 15cm

22.

23.

24.

25. (i)(ii)(iii)

26. (i) 22cm (ii) 28cm (iii) 26cm27. (i) 16cm (ii) 22cm (iii) 16cm28. (i) 2a+b+c (ii) 8a+2b (iii) 2p+q+2r29. (i) b (ii) b (iii) c30. (i) (ii) (iii)31. (i) a (ii) b (iii) m32. (i) a (ii) a (iii) b33. (i) b (ii) a (iii) a34. (i) 44cm (ii) 88cm (iii) 132cm35. (i) 88cm (ii) 44cm (iii) 22cm

mßñ;sh fõ' jfÜ È.hs'mßñ;sh fõ'

yev;, lSmhls 'tllg jvd ;sìh hq;= hs'tlsfklg iïnkaO úh hq;= h'

yrs' jeros' yrs'

tall ,shd ;sìh hq;= hs}

tall ,shd ;sìh hq;= hs}

a + a + b wdldrhg iEfya'



j¾.M,h - I

ld¾h úYaf,aIKh

2'1 cHdñ;sl yev;, y÷kd .ekSu

2'2 ir, cHdñ;sl rEmj, j¾.M,h



j¾.M,h - IwkdjrK mÍlaIKh


m%Yak wruqKq wruqKqwxl wxl

2'1 cHdñ;sl yev;, y÷kd .ekSu'1' 2'1'1 wm wjg we;s øjHj, kï l< yev we| olajhs '2' 2'1'2 È we;s ;, rEm w;=ßka ixjD; ;, rEm f;darhs '3' 2'1'3 § we;s ;, rEm w;=ßka ir, f¾Çh ixjD; ;, rEm f;darhs'4' 2'1'4 § we;s ;, rEm w;=ßka jl% f¾Çh ixjD; ;, rEm f;darhs'5' 2'1'5 § we;s ;, rEm w;=ßka ;%sfldaKdldr rEm f;darhs'6' 2'1'6 § we;s ;, rEm w;=ßka YS¾I fldaK wkqj ;%sfldaKdldr rEm f;darhs'7' 2'1'7 § we;s ;, rEm lSmhla w;=ßka ;%sfldaK fjkafldg olajhs'8' 2'1'8 § we;s ;, rEm w;=ßka p;=ri% f;darhs'9 2'1'9 Ys¾I fldaK wkqj p;=ri% f;darhs'10 2'1'10 ir, f¾Çh ;, rEm lSmhla w;=ßka p;=ri% f;darhs '11' 2'1'11 § we;s ;%sfldaK lSmhla w;=ßka iumdo ;%sfldaK f;darhs'12' 2'1'12 § we;s ;%sfldaK lSmhla w;=ßka iuoaùmdo ;%sfldaK f;darhs'13' 2'1'13 § we;s ;%sfldaK lSmhla w;=ßka úIu ;%sfldaK f;darhs'14' 2'1'14 § we;s ;%sfldaK lSmhla w;=ßka RcqfldaKS ;%sfldaK f;darhs'15' 2'1'15 § we;s p;=ri% lSmhla w;=ßka YS¾I fldaK RcqfldaK jk p;=ri%

f;darhs'16' 2'1'16 § we;s p;=ri% lSmhla w;=ßka iup;=ri%% f;darhs'17' 2'1'17 § we;s p;=ri% lSmhla w;=ßka RcqfldaKdi%% f;darhs'18' 2'1'18 § we;s p;=ri% lSmhla w;=ßka frdïni f;darhs'19' 2'1'19 § we;s p;=ri% lSmhla w;=ßka iudka;rdi% f;darhs'20' 2'1'20 § we;s f;dr;=re wkqj p;=ri% lSmhla w;=ßka ;%mSishï f;darhs'21' 2'1'21 § we;s rEm w;=ßka mßñ;shla iys; rEm f;darhs'22' 2'1'22 § we;s rEm w;=ßka j¾.M,hla iys; rEm f;darhs'23' 2'1'23 § we;s rEm w;=ßka ixjD; ;, rEm f;darhs'24' 2'1'24 m%ldY lSmhla w;=ßka ;, rEmhl mßñ;sh fyda j¾.M,h ms<sn|

±lafjk m%ldYh f;darhs'25' 2'1'25 wjg mßirfha yev;, 2 la w;=ßka j¾.M,fhka úYd, yev;,h

f;darhs'2'2 ir, cHdñ;sl rEmj, j¾.M,h'

26' 2'2'1 iup;=ri%dldr fldgq iys; rEmhl mrsñ;sh fldgq weiqrska ,shd olajhs'27' 2'2'2 iup;=ri%dldr fldgq iys; rEmhl j¾.M,h " fldgqjl j¾.M,h

tall tlla f,i i,ld m%ldY lrhs'28' 2'2'3 iup;=ri%dldr fldgq iys; rEmhl j¾.M,h wNsu; tall j,ska

j.=jl olajhs'29' 2'2'4 fldgq cd,hla u; we| we;s ;%sfldaKhl j¾.M,h o< jYfhka wNsu;

tallj,ska olajhs'30' 2'2'5 mdoj, ñkqï ,l=Kq l< rEmj, j¾.M,h ±laùug Ndú;jk tall

,shd olajhs'



j¾.M,h IwkdjrK mÍlaIKh

m%Yak m;%h

1' wjg mßirfha olakg ,efnk øjH we;=<;a my; j.=j iïmQ¾K lrkak'

yevh w¢kak.=refïi ,E,af,a u;=msg

l¿ ,E,a, u;=msg

f.ìu

odÿleghl uqyqK;

fíifï m;=,

lsß áka tll uqyqK;

úys; p;=ri%h

2' my; ±lafjk rEm w;=ßka ixjD; ;, rEm f;dard tu rEmj,g háka brlaw¢kak'

3' my; ±lafjk rEm w;=ßka ixjD; rEm f;dard tu rEmj,g háka brla w¢kak'

4' my; ±lafjk rEm w;=ßka jl% f¾Çh rEm f;dard tu rEmj,g háka brlaw¢kak'

( i )

(ii )

(iii )

( iv )

( v )

( vi )

(vii )



5' my; ±lafjk rEm w;=ßka ir, f¾Ld LKav ;=klska muKla iEÿKq rEm f;dardtu rEmj,g háka brla w¢kak'

6' YS¾I fldaK ;=kla iys; ir, f¾Çh ixjD; rEm" my; rEm w;ßka f;dard tutla tla rEmhg háka brla w¢kak'

7' my; ±lafjk rEm w;=ßka ;%sfldaK f;dard tajd háka brla w¢kak'

8' my; ±lafjk rEm w;=ßka ir, f¾Ld LKav y;rlska muKla iEÿKq ixjD;;, rEm f;dard tu tla tla rEmhg háka brla w¢kak'

9' my; ±lafjk rEm w;=ßka YS¾I fldaK y;rla muKla we;s ixjD; ;, rEmf;dard" tu tla tla rEmhg háka brla w¢kak'

10' my; ±lafjk rEm w;=ßka p;=ri% f;dard" tu tla tla rEmhg háka brlaw¢kak'



3cm

4cm

6cm5cm

4cm

3cm

11' my; ±lafjk rEm w;=ßka iumdo ;%sfldaK f;dard" tu tla tla rEmhg hákabrla w¢kak'

4 cm 5 cm

4 cm

5 cm

5 cm

12' my; ±lafjk ;%sfldaK w;ßka iu oaùmdo ;%sfldaK f;dard" tu tla tlarEmhg háka brla w¢kak'

13' my; ±lafjk ;%sfldaK w;ßka " úIu ;%sfldaK f;dard tu tla tla rEmhgháka brla w¢kak'

14' my; ±lafjk ;%sfldaK w;ßka " RcqfldaKsl ;%sfldaK f;dard tu tla tlarEmhg háka brla w¢kak'

15' my; ±lafjk rEm w;=ßka YS¾I fldaK RcqfldaK jQ p;=ri% f;dard" tu tla tlarEmhg háka brla w¢kak'

16' my; ±lafjk rEm w;ßka iup;=ri% f;dard" tu tla tla rEmhg háka brlaw¢kak'

5cm

5cm

5cm

5cm

5cm

2cm

4cm 4cm

3cm

4cm

5cm



17' my; ±lafjk rEm w;ßka RcqfldaKdi% f;dard" tu tla tla rEmhgháka brlaw¢kak'

4cm

2cm 2cm

5cm

2cm

18' my; ±lafjk rEm w;ßka frdïni f;dard" tu tla tla rEmhg háka brlaw¢kak'

5cm 4cm

2cm

2cm

2cm

2cm

19' my; ±lafjk rEm w;ßka iudka;rdi% f;dard" tu tla tla rEmhg háka brlaw¢kak'

20' my; ±lafjk rEm w;ßka ;%mSishï f;dard" tu tla tla rEmhg háka brlaw¢kak'

21' my; ±lafjk rEm w;ßka jfÜ È.la .;yels rEm f;dard" tu tla tla rEmhgháka brla w¢kak'

22' my; ±lafjk rEm w;ßka jgjk bv m%udKhla wvx.= rEm f;dard" tu tla tlarEmhg háka brla w¢kak'

5cm

5cm

2cm2cm



( i )

( ii )

( iii )

23' my; ±lafjk rEm w;ßka jfÜ È.la yd jgjQ bv m%udKhla iys; rEm f;dard"tu tla tla rEmhg háka brla w¢kak'

24' my; yd ys " m%ldYhg .e<fmk wjia:dj hk wjia:dw;=ßka f;dard ksjerÈ W;a;rhg háka brla w¢kak'

;, rEmhl jgjk bv m%udKh m%ldY jkafka "mßñ;sfhka 'j¾.M,fhka 'YS¾I fldaK j,ska '

;, rEmhl jfÜ È. m%ldY jkafka "mßñ;sfhka 'j¾.M,fhka 'YS¾I fldaKj,ska '

25' my; ±lafjk tla tla yev;,j, j¾.M, hq., ne.ska jvd úYd, j¾.M,hwh;a yev;,h j.=fõ wod< fma<sfha ysia;ek u; ,shkak'

j¾.M,h ±lafjk yev;, hq.,h' jvd úYd, j¾.M,hwh;a yev;,h

.=refïi ,E,af,a u;=msgyd mka;s ldur f.ìu ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

odÿleghl uqyqK; yd.=refïi ,E,af,a u;=msg ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

.Ks; fm<fmdf;a msgqjyd m;a;r msgqj '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

26' my; ±lafjk rEmj, l=vd fldgqjl me;a;l È. tall tlla f,i f.k tlatla rEmfha mßñ;sh ysia ;ek u; ,shkak'

'''''''''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''''

a. b. ( i ) ( ii ) (iii )

a.( i )( ii )( iii )

b.( i )( ii )( iii )



27' my; ±lafjk rEmj, l=vd fldgqjl j¾.M,h j¾. tall 1 f,i i,lñka "tu rEmj, j¾.M, fidhd rEmhg háka ysia;ek u; ,shkak'

'''''''''''''''''''''''''' ''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''

2 8'

by; rEm weiqfrka my; j.=j iïmQ¾K lrkak' mßñ;h i|yd fldgqjl È.tall 1 la f,i;a " j¾.M,h i|yd l=vd fldgqjl j¾.M,h j¾. tall 1 laf,i;a i,lkak'

rEmh mßñ;sh j¾.M,h

''''''''''''''''''''' '''''''''''''''''''''''

''''''''''''''''''''' '''''''''''''''''''''''

''''''''''''''''''''' '''''''''''''''''''''''

29' my; oelafjk fldgq cd,lh ;=< we;<;a lr we;s ;%sfldaKdldr rEmj,skajgjk j¾.M,h " fldgq .Kka lr ysia ;eka u; ,shkak' fldgqjlska fldgia.Kka lsÍfï § nd.hlg jvd jeä kï tlla f,i;a " fldgqjla j¾. tallhlaf,i;a i,lkak'

a b c

a

b

c

a.

b.

c.

a. ..................

b. ..................

c. ..................



( i ) ( ii ) ( iii )

( iv ) ( v ) ( vi )

30' my; ±lafjk ñkqï iys; rEmj, j¾.M,h ,nd .ekSfï § tu j¾.M, ,shdolajk tallh tu tla tla rEmhg háka ,shkak '

''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''

5cm 5cm

2cm4 cm

10cm

4m

2m

tall 3

tall 3

tall 4



j¾.M,h IwkdjrK mÍlaIKhW;a;r yd Wmfoia

m%Yakwxlh W;a;r Wmfoia

1' yevh y÷kdf.k tu yevho< rEmhlska wÈhs'

2'

3'

4'

5'

6'

7'

8'

9'

i. v.

ii vi.

iii' vii.

iv

m%Yak wxl 2 - 10 f;la oSwe;s rEmj,ska " wod<rEmj,g háka brla we|;sìh hq;= h'

jegySulska f;drj rEm,l=Kq lr ;sfnk njfmfka kï ie,ls<su;a úhhq;= h'

tjeks YsIHhka iïuqLidlÉPdjlg fhduqlr.ksñka ixjD; yd újD; njms<sn| j m%Yak úuikak'


wkdjrK mÍlaIK ñkqïm%Yakwxlh W;a;r Wmfoia

10'

11'

12'

13'

14'

15'

16'

5cm

5cm 5cm

5cm

17'

2cm 2cm 2cm

5cm

4cm

4cm

18'

4cm

2cm

2cm

2cm

2cm

19'

5cm

5cm

2cm

2cm

20'

21'

22'

23'

rEmj, mdo yd fldaK u; i,l=Kqlr we;s ixfla; yÿkd .ekSu yd tuixfla; wkqj rEmh kï lsßfïyelshdj'

j¾.M,h we;=<;a .eg¨j, § mdo u;i,l=Kq lrk ,o ixfla; u.ska rEmy÷kd.; yels ùu wfmalaIs;hs'

jfÜ È.la ,nd .ekSug ixjD;rEmhla ;sîu w;HjYH fõ'rEmfhka jgjk bv m%udKh i|ydixjD; rEmhla u úh hq;= h'jfÜ È.;a " jgjk j¾.M,h;a hkfol u tl u ;, rEmhl tljr;sfnk nj ms<sn| wjOdkh fhduqlrkak'

4 cm

4 cm

5 cm 5 cm

5 cm

3cm 4cm

5cm

5cm

4cm

3cm

5cm

4cm

3cm



24' j¾.M,fhkamßñ;sfhka

25' mka;s ldur f.ìu.=refïi ,E,af,a u;=msgm;a;r msgqj

26' tall 14tall 12tall 16

27' j¾. tall 12j¾. tall 9j¾. tall 7

28' rEmh mßñ;sh j¾.M,htall 16 j¾. tall 16tall 16 j¾. tall 15tall 16 j¾. tall 7

29' j¾. tall 6j¾. tall 5j¾. tall 9

30' j¾. fikaáóg¾ fydaj¾. fikaáóg¾ fydaj¾. fikaáóg¾ fydaj¾. óg¾ fydaj¾. tallj¾. tall

a.b.

( i )( ii )( iii )

( i )( ii )( iii )( i )( ii )( iii )

a b c( a )( b )( c )( i ) cm2

( ii ) cm2

( iii ) cm2

( iv ) m2

( v )( vi )

rEmhlska jgjk bv m%udKhtys j¾.M,h f,i;a " jfÜÈ. mßñ;sh f,i;a ksrjq,a jwjfndaO ù ;sìh hq;= h' tfiafkdue;s nj fmfka kïiïuqL idlÉPdjlg fhduqlsÍu wjYH fõ'j¾.M,h iei£ug mßirfhawe;s ;, rEmj, m%udKhms<sn| jegySu wfmalaIs; hs'

fldgqjl È. tallh f,iie,fla'

y;/ia fldgqjl j¾.M,hj¾. tallhla f,i ie,fla'

mßñ;sh iudk jqj;a j¾.M,hfjkia úh yels nj'

ms<s;=r wdikak fldgq .Kkf,i ;sîu iEfya'

È. ñkqï wkqj j¾.M,h iu.tallh ielfik nj'



j¾.M,h - II

ld¾h úYaf,aIKh

2'3 RcqfldaKdi%j, j¾.M,h

2'4 ;%sfldaKj, j¾.M,h

2'5 iudka;rdi%j, j¾.M,h

2'6 ;%mSishul j¾.M,h



j¾.M,h IIwkdjrK mÍlaIKh -

iúia;r ld¾h úYaf,aIKh


2'3 RcqfldaKdi%hl j¾.M,h'1' 2'3'1 RcqfldaKdi%hl È. yd m<, ñkqï § we;s úg tu ñkqï weiqßka tys

j¾.M,h ms<sn| m%ldYhla ,shhs'2 2'3'2 RcqfldaKdi%hl os. yd m<, oS we;s úg tys j¾.M,h fidhhs'3 2'3'3 RcqfldaKdi%hl j¾.M,h yd m<, § we;s úg RcqfldaKdi%fha È.

i|yd m%ldYkhla ,shhs'4' 2'3'4 RcqfldaKdi%hl j¾.M,h yd m<, § we;s úg È. .Kkh lrhs'5' 2'3'5 mdoj, ñkqï § we;s úg iup;=ri%hl j¾.M,h fiùu i|yd

m%ldYkhla" § we;s ñkqï weiqßka ,shhs'6' 2'3'6 mdoj, ñkqï § we;s iup;=ri%hl j¾.M,h fidhhs'7' 2'3'7 j¾.M,h § we;s iup;=ri%hl me;a;l È. fiùu i|yd m%ldYkhla" §

' we;s ñkqï weiqßka ,shhs'8' 2'3'8 j¾.M,h § we;s iup;=ri%hl me;a;l È. fidhhs'

2'4 ;%sfldaKhl j¾.M,h'9' 2'4'1 mdoj, ñkqï § we;s RcqfldaKS ;%sfldaKhl j¾.M,h ±laùu i|yd

m%ldYkhla ,sùug wjYH ñkqï muKla ,shd olajhs'10' 2'4'2 RcqfldaKS ;%sfldaKhl mdoj, ñkqï § we;s úg" § we;s ñkqï weiqßka

;%sfldaKfha j¾.M,h i|yd m%ldYkhla ,shd olajhs'11' 2'4'3 RcqfldaKS ;%sfldaKhl mdoj, ñkqï § we;s úg" tlsfkl ,ïn mdo

y÷kd .ksñka ;%sfldaKfha j¾.M,h .Kkh lrhs'12' 2'4'4 RcqfldaKS ;%sfldaKhl j¾.M,h yd RcqfldaKh wvx.= mdo foflka

tll È. § we;s úg tys j¾.M,h iólrKhlska ,shd olajhs'13' 2'4'5 RcqfldaKS ;%sfldaKhl j¾.M,h yd RcqfldaKh wvx.= mdo foflka

tll È. § we;s úg tys wfkla mdofha È. .Kkh lrhs'14' 2'4'6 YS¾Ihl isg mdohlg ,ïnhla we| we;s ;%sfldaK lSmhl wdOdrl

mdoh yd ,ïN Wi y÷kd f.k j.= .; lrhs'15' 2'4'7 ;%sfldaKhl § we;s ñkqï w;ßka tys j¾.M,h fiùug wjYH ñkqï

f;dardf.k ,shd olajhs'16' 2'4'8 ;%sfldaKhl wdOdrlh yd ,ïn Wfiys ñkqï § we;s úg tu ñkqï

weiqßka j¾.M,h fiùu i|yd m%ldYkhla ,shhs'17' 2'4'9 ;%sfldaKhl wdOdrlh yd ,ïn Wfiys ñkqï § we;s úg tys j¾.M,h

.Kkh lrhs'18' 2'4'10 ;%sfldaKhl j¾.M,h yd wdOdrlfha Èf. ys ñkqï § we;s úg iy

,ïn Wi ùÔh ixfla;hlska olajd we;s úg tu rdYSka w;riïnkaOh iólrKhlska olajhs'

19' 2'4'11 ;%sfldaKhl j¾.M,h yd wdOdrlfha ñkqï § we;s úg ;%sfldaKfha,ïn Wi .Kkh lrhs'



20' 2'4'12 ;%sfldaKhl j¾.M,h yd ,ïn Wfiys ñkqï § we;s úg wdOdrlfhaÈ.,nd .ekSug wjYH m%ldYkh ,shd olajhs '

2'5 iudka;rdi%j, j¾.M,21' 2'5'1 iudka;rdi%hl mdoj, ñkqï yd mdo w;r ,ïn ÿr § we;s úg tu ñkqï

w;ßka ,ïn ÿr ±lafjk ñkqu y÷kd f.k ,shd olajhs'22' 2'5'2 mdoj, È. yd ,ïn ÿr ,l=Kq l< rEm w;=ßka" j¾.M,h fiùug wjYH

ñkqï iys; rEm y÷kd f.k ,shd olajhs'23' 2'5'3 iudka;rdi%hl mdoj, È. yd mdo folla w;r ,ïn ÿr § we;s úg tu

ñkqï weiqßka j¾.M,h fiùug m%ldYkhla ,shd olajhs'24' 2'5'4 frdïnihl mdohl È. yd mdo folla w;r ,ïn ÿr § we;s úg

frdïnifha j¾.M,h .Kkh lrhs'25' 2'5'5 frdïnihl j¾.M,h yd mdohl ñkqï § we;s úg mdo folla w;r ,ïn

ÿr i|yd m%ldYkhla § we;s ñkqï weiqßka ,shhs'26' 2'5'6 frdïnihl j¾.M,h yd wdOdrlfha ñkqï § we;s úg mdo w;r ,ïn

ÿr .Kkh lrhs'27' 2'5'7 iudka;rdi%hl noaO mdo foll iy mdo folla w;r ,ïn ÿr § we;s úg

tu ñkqï weiqßka tys j¾.M,h fiùu i|yd m%ldYkhla ,shhs'28' 2'5'8 iudka;rdi%hl noaO mdo foll iy mdo folla w;r ,ïn ÿr § we;s úg

tys j¾.M,h .Kkh lrhs'29' 2'5'9 iudka;rdi%hl mdohla fyda mdo folla w;r ,ïn ÿr iuÕ j¾.M,h §

we;s úg mdo folla w;r ,ïn ÿr fyda mdohl È. iïnkaO m%ldYkhla§ we;s ñkqï weiqßka ,shd olajhs'

2'6 ;% smSishul j¾.M,h'

30' 2'6'1 ;%mSishul iudka;r mdo foflys iy tu mdo fol w;r ,ïn ÿfrysñkqï § we;s úg tu ñkqï weiqßka ;%mSishfï j¾.M,h ±laùu i|ydm%ldYkhla ,shd olajhs'

31' 2'6'2 ;%mSishul iudka;r mdo foflys iy tu mdo fol w;r ,ïn ÿfrysñkqï § we;s úg tys j¾.M,h .Kkh lrhs'

32' 2'6'3 ;%mSishul j¾.M,h iy iudka;r mdo foflys ñkqï § we;s úg iyiudka;r mdo fol w;r ,ïn ÿr ùÔh ixfla;hla u`.ska olajd we;s úgtu rdYSka w;r iïnkaOh iólrKhla u`.ska olajhs'

33' 2'6'4 ;%mSishul j¾.M,h iuÕ iudka;r mdo foflka tll È. iyiudka;r mdo fol w;r ,ïn ÿr § we;súg b;sß iudka;r mdofha È.fiùug iqÿiq iólrKhla f.dvkÕhs'

34' 2'6'5 ;%mSishul j¾.M,h " iudka;r mdo fol w;r ,ïn ÿr iy tlaiudka;r mdohl ñkqï § we;s úg wfkla iudka;r mdofha È. .Kkhlrhs'



wkdjrK mÍlaIKhj¾.M,h - ii

m%Yak m;%h

1' my; ±lafjk tla tla RcqfldaKdi%fha j¾M,h ,nd .ekSug wod< m%ldYkhla§ we;s ñkqï wkqj ,shkak' ^ iq¿ lsÍu wjYH ke;' &

a m

10cm

5cm

4cm

6cm

b m

'''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''

2' my; ±lafjk tla tla RcqfldaKdi%fha j¾.M,h fidhkak'

6cm 10cm

5cm 4cm

5 m

2 m

''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''

3' j¾.M,h yd m<, § we;s my; ±lafjk RcqfldaKdi%fha È. fiùu i|yd § we;sñkqï wkqj m%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &

72m2 35 cm2

40 cm2 4cm

5cm

8 m

''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''

4' j¾.M,h yd m<, § we;s my; ±lafjk RcqfldaKdi%fha È. fidhkak'

72m2 35 m2

40cm2 4cm

5 m

8 m

'''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''

i. ii. iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.



5' my; ±lafjk tla tla iup;=ri%fha j¾.M,h fiùu i|yd § we;s ñkqï wkqjm%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &

5cm

5cm

5cm

5cm

6cm

6cm

6cm 6cm

x cm

'''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''

6' my; olajd we;s ñkqï wkqj tla tla iup;=ri%fha j¾.M,h fidhkak'

6cm

6cm

6cm 6cm

3 cm

5 m

3 cm 3 cm

3 cm

5 m

5 m

5 m

''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''

7' j¾.M,h § we;s my; ±lafjk tla tla iup;=ri%fha me;a;l È. fiùu i|ydm%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &

100 cm2

49 m2

1 cm2

''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''

8' j¾.M,h § we;s my; ±lafjk tla tla iup;=ri%fha me;a;l È. fidhkak'

100 m2 49 cm2

1 m2

''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''

i . ii . iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.



9' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h ,nd .ekSu i|yd" tu;%sfldaKj, i|yka lr we;s ñkqïj,ska wjYH jk ñkqï muKla f;dard ;s;afm< u; ,shkak'

4 cm

3 cm 5 cm 8 m 6 m

10 m

a m

b m

c m

''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''

10' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h ,nd .ekSu i|yd" §we;s ñkqï we;=<;a m%ldYkhla ;s;afm< u; ,shkak' ^ iq¿ lsÍu wjYH ke;'&

10 cm 4 cm

3 cm 5 cm 8 cm 6 cm

10 cm

8 cm x cm

''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''

11' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h fidhkak'

4 cm

3 cm 5 cm 8 m 6 m

10 m

8 m

10

cm

x m

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

12' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h yd RcqfldaKh wvx.=tla mdohl ñkqï § we;' RcqfldaKh wvx.= wfkla mdoh jk ,nd .ekSui|yd § we;s f;dr;=re we;=<;a iólrKhla ,shkak'

5 cm

x 10 m 8 m 10 cm2

20 m2 16m2 x

x

'''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''

13' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h yd Rcq fldaKh wvx.=tla mdohl ñkqï § we;' RcqfldaKh wvx.= wfkla mdofha È. fidhkak'

5 m

10 cm 8 10 m2

20 cm2 48 cm2

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

x

i. ii. iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.



14' my; ±lafjk tla tla ;%sfldaKfha we;=<;a lr we;s f;dr;=re weiqßka" § we;sj.=j iïmQ¾K lrkak'

A

B D C K N M

R

L P

;%sfldaKh wdOdrl mdoh ,ïn Wi

1. ABC ..................... .......................................2. PQR ..................... .......................................3. KLM ..................... .......................................

15' my; oelafjk ;%sfldaKhkays mdoj, oS we;s ñkqïj,ska tu tla tla;%sfldaKfha j¾.M,h ,nd .ekSu i|yd wjYH jk ñkqï my; ;s;a fm< u;,shkak'

6cm 4cm 6 cm

10 cm

12 m

12m x m 12m 8 cm

6 cm

4 cm

3 cm

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''

16' my; oelafjk tla tla ;%sfldaKhkays j¾.M,h ,nd .ekSu i|yd oS we;s ñkqïiïnkaO lr m%ldYk ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &

10 cm

5 cm

12 cm

8 m

5 m 4 cm

5 cm

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''

Q

S

i. ii. iii.

i. ii. iii.

i. ii. iii.



17' my; oelafjk tla tla ;%sfldaKfha j¾.M,h .Kkh lrkak'

10 m

5 cm

12 cm

8 cm

5 cm 4 m

5 cm

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''

18' my; ±lafjk tla tla ;%sfldaKfha j¾.M,h yd wdOdrl mdofha ñkqï § we;'j,ska ±lafjk ,ïn Wi fiùu i|yd § we;s ñkqï we;=<;a iólrKhla

,shkak'

10 cm

12 m h

h h

8 cm

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''

19' j¾.M,h yd wdOdrl mdoj, ñkqï § we;s my; ±lafjk tla tla ;%sfldaKfha j,ska ±lafjk ,ïn Wi fidhkak'

10 cm

12 m h

h h

8 cm

'''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''20' j¾.M,h yd ,ïn Wi § we;s my; ±lafjk tla tla ;%sfldaKfha f,i

±lafjk wdOdrl mdofha È. ,nd .ekSu i|yd § we;s ñkqï we;=<;a m%ldYkhla,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &

x

x 6 cm

5 m 4 cm

x < >

< >

'''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''

x

= 16 cm2 = 20 cm2 = 36 m2j¾.M,h j¾.M,h j¾.M,h

j¾.M,h j¾.M,h j¾.M,h= 16 cm2 = 50 cm2 = 36 m2

h

h

j¾.M,h j¾.M,h j¾.M,h= 20 cm2 = 24 cm2 = 36 m2

i. ii. iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.



21' my; iudka;rdi%j, olajd we;s ñkqïj,ska" iïuqL mdo w;r ,ïn ÿr ±lafjkñkqu f;dard" ;s;a br u; ,shkak'

12 cm 16 cm

15 cm

12 cm 15 cm

16 cm

12 cm 8 cm Xx 8 cm

15 cm

15 cm 8 cm

'''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

22' my; ±lafjk p;=ri% w;ßka j¾.M,h fiùug m%udKj;a o;a; ,l=Kq l< rEmigyka háka brla w¢kak'

23' my; ±lafjk iudka;rdi%j, olajd we;s ñkqï weiqßka tajdfha j¾.M, ±lafjkm%ldYhla ;s;a bru; ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &

8 cm Xx 8 cm

6 cm

6 cm

10 cm

8 cm 12 cm

15 cm

12 cm

5 cm 8 cm

12 cm

''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''

24' my; ±lafjk tla tla frdïnifha j¾.M,h fidhkak'

6 cm

5 cm 12 cm

12 cm

8 cm

6 cm

10 cm

8cm

''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''

8 cm Xx 8 cm

4 cm

6 cm

4 cm

6 cm 5 cm

6 cm

4 cm

8 cm

6 cm 6 cm

10 cm

5 cm 7 cm

i. ii. iii.

i. ii. iii.

i. ii. iii.

12cm



25' my; ±lafjk tla tla frdïnifha j¾.M,h yd wdOdrl mdofha È. § we;'f,i ±lafjk ,ïn Wi ,nd .ekSu i|yd § we;s ñkqï we;=<;a m%ldYkhla

;s;a br u; ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &

12 cm

12 cm

8 cm

h

10 m

h

9 cm

h

j¾.M,h j¾.M,h j¾.M,h''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

26' my; ±lafjk tla tla frdïnifha j¾.M,h yd wdOdrl mdofha È. § we;' tlatla frdïnifha ,ïn Wi fidhkak'

12 cm

12 cm

8 cm

h

9 cm

h

10 m

h

j¾.M,h j¾.M,h j¾.M,h''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

27' my; ±lafjk tla tla iudka;rdi%fha j¾.M,h ,nd .ekSu i|yd § we;s ñkqïwe;=<;a lrñka m%ldYkhla ne.ska ;s;a br u; ,shkak' ^iq¿ lsÍu wjYH fkdfõ' &

10 cm

5cm 12 cm

12 cm

12 cm

5cm

8 cm 6 cm

6 m

5cm 12 cm

12 cm

10 m 4 m

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''

28' my; ±lafjk tla tla iudka;rdi%fha j¾.M,h fidhkak'

'''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''

h

= 40 m2 = 45 cm2 = 24 cm2

= 40 m2 = 45 cm2 = 24 cm2

10 cm

5cm 12 cm

12 cm

12 cm

5cm

8 cm 6 cm

6 m

5cm 12 cm

12 cm

10 m 4 m

i. ii. iii.

i. ii. iii.

i. ii. iii.

i. ii. iii.



29' my; iudka;rdi%j, j¾.M,h yd ;j;a tla ñkqula olajd we;' j¾.M,hgiïnkaO wfkla ñkqu ,nd .ekSu i|yd" tu ñkqu yd j¾.M,h iïnkaO lrkm%ldYkhla my; ;s;a fm< u; ,shkak'

12 cm

12 cm

6 cm

2 m

10 cm

j¾.M,h j¾.M,h j¾.M,h

''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

30' my; oelafjk tla tla ;%mSishfïj¾.M,h ,nd .ekSu i|yd § we;s ñkqïwe;=<;a m%ldYkhla ;s;a br u; ,shkak' ^ W;a;rh iq¿ lsÍu wjYH fkdfõ' &

>

>

>

> ^

^

^

4 m

5 m

10 m

3 cm

5 cm

9 cm

x

2 m

y

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''

31' my; ±lafjk tla tla ;%mSishfï j¾.M,h fidhkak'

>

>

>

> ^

^

^

4 m

5 m

10 m

3 cm

5 cm

9 cm

x

2 m

y

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''

= 30 cm2 = 24 cm2 = 12 m2

hx

x

i. ii. iii.

i. ii. iii.

i. ii. iii.



32' fuys olajd we;s tla tla ;%mSishfï j¾.M,h yd iudka;r mdo j, ñkqï § we;'iudka;r mdo fol w;r ,ïn ÿr jk ,nd .ekSu msKsi" § we;s f;dr;=rewe;=<;a iólrKhla ;s;a br u; ,shkak' ^ W;a;rh iq¿ lsÍu wjYH fkdfõ' &

>

>

^ ^ >

>

2 m

h

8 m

7 m 5 m

h

4 cm

h

8 cm


'''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

33' fuys olajd we;s tla tla ;%mSishfï j¾.M,h " iudka;r mdo hq.,fhka tll

È. yd iudka;r mdo w;r ,ïn ÿr § we;' tu ñkqï wkqj j,ska olajd we;s

mdofha È. ,nd .ekSu i|yd iqÿiq iólrKhla ,shkak' ^ iólrKh úi£u

wjYH fkdfõ' &

>

>

^ ^ >

>

x

4 m

10 m

x 4cm

5cm

4 m

6 m

x


''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

34' my; ±lafjk tla tla ;%mSishfï j,ska ±lafjk w.h fidhkak'

>

>

^ ^ >

>

x

4 m

10 m

x 4cm

5cm

4 m

6 m

x


''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''

h

x

x

= 40 m2 = 30 m2 = 18 cm2

= 24 m2 = 30 cm2 = 36 m2

= 24 m2 = 30 cm2 = 36 m2

i. ii. iii.

i. ii. iii.

i. ii. iii.



j¾.M,h - 11wkdjrK mÍlaIKh

W;a;r yd Wmfoia

1. i. (510) cm2 ii. (64) cm2 iii. (ab) m2

2. i. 50 cm2 ii. 24 cm2 iii. 10 m2

3. i. 40/4 ii. 35/5 iii. 72/84. i. 10 cm ii. 7 m iii. 9 m5. i. 66 ii. 55 iii. x2

6. i. 36 cm2 ii. 25 m2 iii. 9 cm2

7. i. 2cm100 ii. 2 49m iii. 2cm1

8. i. 10m ii. 7cm iii. 1m9. i. 3cm,4cm ii. 8m,6m iii. am,bm

10. i. 342

1 ii. 86

2

1 iii. 810

2

1

11. i. 6cm2 ii. 24 m2 iii. 40 m2

12. i. 1052

1 x ii. 2010

2

1 x iii. 168

2

1 x

13. i. 4 cm ii. 4 cm iii. 12 cm

14. ;%sfldaKh wdOdrl mdoh ,ïn WiABC BC ADPQR PQ RSKLM KM LN

15. i. 10cm,4cm ii. 12m, x m iii. 8cm,3cm

16. i. 4102

1 ii. 512

2

1 iii. 58

2

1

17. i. 20 m2 ii. 30 cm2 iii. 20 cm2

18. i. 1682

1 h ii. 2010

2

1 h iii. 3612

2

1 h

19. i. h = 4 cm ii. 10 cm iii. 6 m

20. i. 2052

1 x ii.

14 24

2x iii. 366

2

1 x

21. i. 8 cm ii. 12 cm iii. 12 cm

22.

4 cm

6 cm

6 cm

4 cm

8 cm

6 cm 6 cm

10 cm

5 cm 7 cm




23. i. 56 ii. 815 iii. 108

24. i. 30 cm2 ii. 48cm2 iii. 80 cm2

25. i. 4010 h ii. 459 h iii. 248 h

26. i. 4 m ii. 5 cm iii. 3 cm

27. i. 510 ii. 56 iii. 410

28. i. 50 cm2 ii. 30 cm2 iii. 40 m2

29. i. 310 h 0 ii. 246 x iii. 122 x

30. i. 52

104

ii. 5

2

93

iii. 2

2

yx

31. 35 m2 ii. 30 cm2 iii. x+y m2

32. i. 402

)82(

h ii. 30

2

)57(

h

iii. 182

)84(

h

33. i. 2442

)10(

xii. 305

2

)4(

x

iii. 3662

)4(

x

34. 2 m ii. 8 cm iii. 8 cm



mßudj

ld¾h úYaf,aIKh

3'1 >k jia;= y÷kd.ekSu

3'2 >klhl yd >kldNhl mßudj

3'3 ;%sfldaK ms%siauhl mßudj



3' mrsudjwkdjrK mÍlaIKh

iúia;rd;aul ld¾h úYaf,aIKhm%Yak wruqKq Wmfoiawxlh wxlh

3'1 >k jia;= y÷kd.ekSu'1' 3'1'1 fok ,o ,ehsia;=jlska ;, rEm yd >kjia;= fjka lr olajhs'2' 3'1'2 fok ,o øjH ish,a,gu wjldYfha bvla wjYH jk nj m%ldY lrhs'3' 3'1'3 mßirfha olakg we;s úúO >k jia;+j, uQ,sl yevh y÷kajk ku

,shd olajhs'4' 3'1'4 ñkqï olajd we;s >klhl" me;a;l È. fjka lr ,shd olajhs'5' 3'1'5 ñkqï olajd we;s >klhl È." m<, yd Wi fjka fjka j ,shd olajhs'

3'2 >klhl yd >kldNhl mßudj6' 3'2'1 leghla weiqßka " Wi jQ úúO m%udKfha >kldNj, mßudj

,shd olajhs'7' 3'2'2 Wi jQ >kldNhl mßudj .Kkh lrhs'8' 3'2'3 fikaáógr tallj,ska ñkqï § we;s >kldNhl mßudj .Kkh lrhs'9' 3'2'4 ñkqï tall ógrj,ska § we;s >kldNhl mßudj .Kkh lrhs'10' 3'2'5 >klhl mßudj .Kkh lrhs'11' 3'2'6 fok ,o >k jia;=jl ;,hlg iudka;r j ,efnk yrialv tl u

m%udKfhka yd tl u yevfhka hqla; nj ksÍlaIKh lr m%ldY lrhs'12' 3'2'7 fok ,o >kjia;=j, taldldr yrialvla mj;sk nj fyda fkdmj;sk

nj m%ldY lrhs'13' 3'2'8 fok ,o >kldNhl " § we;s ñkqï wkqj yrialv j¾.M,h .Kkh

lrhs'14' 3'2'9 fok ,o >kldNhl taldldr yrialv j¾.M,h Wi" f,i f.k

mßudj .Kkh lrhs'15' 3'2'10 >kldNhl § we;s ñkqï w;ßka yrialv j¾.M,h fidhd mßudj

.Kkh lrhs'16' 3'2'11 yrialv j¾.M,h j¾. fikaáógrj,ska yd È. fyda Wi fikaáógr

j,ska § we;s >kldNhl mßudj .Kkh lrhs'17' 3'2'12 yrialv j¾.M,h j¾. fikaáógrj,ska yd È. fyda Wi ógrj,ska §

we;s >kldNhl mßudj .Kkh lrhs'

3'3 ;%sfldaK m%siauhl mßudj18' 3'3'1 ñkqï § we;s ´kE u RcqfldaKsl ;%sfldaKhl j¾.M,h .Kkh lrhs'19' 3'3'2 fok ,o ´kE u ;%sfldaKhl" wdOdrlh yd ,ïn Wi u`.ska j¾.M,h

.Kkh lrhs'20' 3'3'3 ;%sfldaK m%siauhl taldldr yrialv w÷re lr fmkajhs'21' 3'3'4 yrialv yevh wkqj m%siau kï lrhs'22' 3'3'5 RcqfldaKsl ;%sfldaK m%siauhl yrialv j¾.M,h .Kkh lrhs'23' 3'3'6 RcqfldaKsl ;%sfldaK m%siauhl mßudj .Kkh lrhs'24' 3'3'7 § we;s ñkqï weiqßka" ;%sfldaK m%siauhl yriallv j¾.M,h .Kkh

lrhs'

1 cm3 1 cm

1 cm



25' 3'3'8 ;%sfldaK m%siauhl mßudj .Kkh lrhs'26' 3'3'9 ;%sfldaK m%siauhl mßudj yd yrialv j¾.M,h § we;s úg tys Wi

.Kkh lrhs'27' 3'3'10 ;%sfldaK m%siauhl mßudj iu. Wi fyda È. ÿka úg tys yrialv

j¾.M,h .Kkh lrhs'28' 3'3'11 Rcq m%siau we;=<;a .eg¨ úi|hs'



mßudjwkdjrK mÍlaIKh

m%Yak m;%h'

1' my; oelafjk j.=fõ tla tla y÷kajdfok ku wh;a jk ;Srej f;dard o"wfkla ;Srhg o fhdokak'

y÷kajdfok ku ;, rEmhls >kjia;=jlsiup;=ri%h>klh>kldNhRcqfldaKdi%hjD;a;his,skavrhf.da,hiudka;rdi%h;%sfldaKh

2' my; oelafjk j.=fõ ±lafjk tla tla øjH wjldYfha .kakd bv ms<sn|j".e,fmk ;Srefõ ,l=K o " wfkla ;Srefõ ,l=K o fhdokak'

y÷kajdfok ku wjldYfha wjldYfhabvla .kshs' bvla fkd.kshs'

.fvd,a leghlvodishfnda,hud¿ ákatlúiaflda;= fmÜáhíf,aâ ;,hfmd;ulklE,a,

3' my; j.=fõ ±lafjk >k jia;=j, yevh y÷kajk ku ,shkak'

>kjia;=j yevh y÷kajk ku



>k jia;=j yevh y÷kajk ku

iv

v

vi

4' my; oelafjk j.=fõ >klj, § we;s ñkqï weiqßka j.=j iïmQ¾K lrkak'

>klh >klfha me;a;l È.

1 cm

1 cm 1 cm

1 cm

2 cm

2 cm

2 cm 2 cm

3 cm

3 cm

3 cm

3 cm

5' my; >kldNj, § we;s ñkqï wkqj " my; oelafjk j.=j iïmQ¾K lrkak'

>kldNh È. m<, Wi

2 cm 1 cm

1 cm

2 cm

1 cm

3 cm

1 cm

4 cm

2 cm



6' fuu >kl yev;s legfha mßudj >kfikaá óg¾ 1 f,i i,ldmy; oelafjk tla tla >kldNj, mßudj we;=<;a lrñka j.=jiïmQ¾K lrkak'

>kldNh È. m<, Wi leg .Kk mßudj

2cm 1cm 1cm

3cm 1 cm 1cm

3cm 2cm 1cm

1 cm3

7' my; j.=fõ ±lafjk ñkqï wkqj j.=j iïmQ¾K lrkak '

>kldNfha ñkqï >kldNfha mßudjÈ. m<, Wi È. m<, Wi mßudj

i. 1cm 1cm 1cm 111 1 cm3

ii. 2cm 1cm 1cm

iii. 2cm 2cm 1cm

iv. 5cm 2cm 1cm

v. 8cm 5cm 1cm

8' oS we;af;a >kldNhkaf.a ñkqï h' tajdg wkqj j.=j iïmQ¾K lrkak'

È. m<, Wi È. m<, Wi mßudj

i. 5cm 4cm 1cm 541 20 cm3

ii. 10cm 4cm 5cm

iii. 8cm 7cm 10cm

iv. 12cm 8cm 10cm

9' oS we;af;a >kldNhkaf.a ñkqï h' tajdg wkqj j.=j iïmQ¾K lrkak'

È. m<, Wi È. m<, Wi mßudj

i. 5m 2m 1m 521 10 cm3

ii. 4m 2m 2 m

iii. 10m 5 m 3m

iv. 8 m 5 m 4 m

v. 12m 8 m 4 m



10' my; j.=fõ ±lafjkafka >kldNhl ñkqï h' tla tla >kldNj, ñkqïweiqßka j.=j iïmQ¾K lrkak'

me;a;l È. me;a;l È. me;a;l È. me;a;l È. mßudj

3 cm 3 3 3 27 cm3

5 cm

10 cm

12 cm

20 cm

11' my; oelafjk tla tla >k jia;=j ksÍlaIKh lsÍfuka " tys w÷re lr we;syrialv Bg iudka;r j w¢k ,o ´kE u ;,hl yrialvg m%udKfhka yd

yevfhka iudk jk fyda fkdjk nj wkqj j.=j iïmQ¾K lrkak'

>k jia;=j yrialv" m%udKfhka yrialv" m%udKfhkayd yevfhka iudk h' yd yevfhka wiudk h'

i.

ii.

iii.

iv.

v.

12' my; oelafjk j.=j fyda fhdoñka iïmQ¾K lrkak'>kjia;=j taldldr yrialvla ;sfí' taldldr yrialvla ke;'>klh>kldNhiup;=ri% ms%iauh;%sfldaK ms%iauhfla;=jis,skavrh



13' my; oelafjk tla tla >kldNfha w÷relr fmkajd we;s yrialv j¾.M,hfidhkak'

>kldNh yrialv j¾.M,h

i. 2 cm

3 cm

5 cm

ii.

5 cm

4 cm

3 cm

iii.

10 cm

2 cm

5 cm

my; oelafjk A,B,C,D >kldN weiqßka m%Yak 14 yd 15 ys j.= iïmQ¾Klrkak'

14' >kldNh È. m<, Wi mßudj

i. A 5 cm 2cm 2 cm 3(2 2) 5 20cm

ii. B 8cm 6 cm 10cm ......... ..........= ........... cm3

iii. C ..... ..... ..... ......... ..........= ........... cm3

iv. D .... .... ..... ......... ..........= ........... cm3

......... ..........= ........... cm2

......... ..........= ........... cm2

......... ..........= ........... cm2

2 cm

2 cm

5 cm

8 cm

6 cm

10cm

5 cm

5 cm

5 cm

5 cm

12 cm

2 cm

8 cm

A B C

D

w÷re l< fldgfia j¾.M,h



15' >kldNh yrialv j¾.M,h Wi$È. mßudj =yrialv j¾.M,hWi

i. A 22 = 4 cm2 5 cm 4 5 = 20 cm3

ii. B 8 6 = ....... 10 cm ......................................

iii. C ..............= ........ 5 cm .....................................

iv. D ..............= ........ 12 cm .....................................

16' yrialv j¾.M,h yd Wi fyda È. § we;s my; j.=fõ oelafjk tla tla>kldNj, mßud fidhd j.=j iïmQ¾K lrkak'

yrialv j¾.M,h Wi fyda È. mßudj2 340 cm 12 cm 40 12 = 480 cm 2 310 cm 8 cm ............= ....... cm 2 325 cm 3 cm .............= ........ cm

2 3100 cm 24 cm .......... = ........ cm

17' yrialv j¾.M,h yd Wi fyda È. § we;s my; oelafjk j.=fõ tla tla>kldNj, mßudj we;=<;a lrñka j.=j iïmQ¾K lrkak'

yrialv j¾.M,h Wi fyda È. mßudj

10 m2 5 m 310 5 50m 6 m2 4 m ............................20 m2 12 m ............................18 m2 10 m ............................

18' my; oelafjk tla tla RcqfldaKS ;%sfldaKj, j¾.M, we;=<;a lrñka j.=jiïmQ¾K lrkak'

RcqfldaKS ;%sfldaKh j¾.M,h 1

2 wdOdrlh ,ïn Wi

i.

10 cm

8 cm

2110 8 40

2cm

ii.

6 cm 8 cm

10 cm ...............................................



RcqfldaKS ;%sfldaKh j¾.M,h 1

2 wdOdrlh ,ïn Wi

iii.

4 cm

10 cm .....................................................

iv.

5 cm

12 cm

13 cm

....................................................

19' my; oelafjk tla tla ;%sfldaKj, j¾.M, fidhd j.=j iïmQ¾K lrkak'

;%sfldaKh1

2 wdOdrl mdofha È. ,ïn Wi = j¾.M,h

i.

5 cm 4 cm

10 cm

2110 4 20

2cm

ii.

12 cm

5 cm 21

....... ....... ..............2

cm

iii.

6 cm 10 cm

5 cm

..............................................

iv.

12 cm

6 cm

7 cm

..............................................



20'my; oelafjk tla tla ;%sfldaK m%siaufha taldldr yrialv w÷re lrkak'

21' my; oelafjk tla tla Rcq m%siauh" tys yrialv wkqj kï lrñka ysia;ekaiïmQ¾K lrkak'

i. RcqfldaKS ;%sfldaK yrialvla iys; Rcq m%siauhls'

ii.

'''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'

iii. '''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'

iv.

'''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'

22' my; oelafjk tla tla RcqfldaKS ;%sfldaK m%siaufha yrialv j¾.M,h" § we;sysia;eka iïmQ¾K lrñka ,nd .kak'

5 cm

3 cm

4 cm

(i.) (ii.) (iii.)

(iv.)

yrialv j¾.M,h

2

1....... .......

2

..............cm



ii. 6 cm

8 cm

14 cm

10 cm

iii.

5 cm

12 cm

13 cm

15 cm

23' 22 m%Yakfhys we;=<;a (i) , (ii), (iii) ;%sfldaK m%siauj, mßudj my; ysia;ekaiïmQ¾K lrñka ,nd.kak'

i. mrsudj = yrialv j¾.M,h È.= ............. x ............= ............... cm3

ii.

iii.

24' my; oelafjk tla tla ;%sfldaK m%siauj, yrialv j¾.M,h § we;s ysia;ekaiïmQ¾K lrñka ,nd .kak'

i.

10 cm

8 cm

6 cm

ii.

10 cm

12 cm

4 cm

yrialv j¾.M,h

2

1....... .......

2

..............cm

yrialv j¾.M,h

2

1....... .......

2

..............cm

xmrsudj = yrialv j¾.M,h È.= ............. x ............= ............... cm3

mrsudj = yrialv j¾.M,h È.= ............. x ............= ............... cm3

yrialv j¾.M,h

2

1...... ........

2

.................cm

yrialv j¾.M,h

2

1...... ........

2

.................cm



iii.

20 cm

8 cm

12 cm

25' 24 m%Yakfha oelafjk tla tla m%sfldaK m%siauj, mßudj my; § we;s ysia;ekaiïmQ¾K lrñka ,nd.kak'

i. ;s%fldaK m%siaufha mßudj

3

........ ..........

.................cm

ii. ;s%fldaK m%siaufha mßudj

3

........ ..........

.................cm

iii. ;s%fldaK m%siaufha mßudj

3

........ ..........

.................cm

26' my; oelafjk j.=fõ § we;s ;%sfldaK m%siauj,g wod< f;dr;=rej,g wkqj tysysia;eka iïmQ¾K lrkak'

mßudj yrialv j¾.M,h È. ,nd.kakd wdldrh È.

i. 200 cm3 40 cm2

200

40 5 cm

ii. 120 cm3 30 cm2 .................................................... ........................

iii. 48 cm3 12 cm2 ................................................... .........................

iv. 220 cm3 20 cm2 .................................................. ........................

yrialv j¾.M,h

2

1...... ........

2

.................cm

yrialv j¾.M,h Wi

yrialv j¾.M,h Wi

yrialv j¾.M,h Wi



27' my; oelafjk j.=fõ § we;s ;%sfldaK m%siauj,g wod< f;dr;=rej,g wkqj tysysia;eka iïmQ¾K lrkak'

mßudj È. yrialv j¾.M,h yrialv j¾.M,h,nd.kakd wdldrh

400 cm3 5 cm400

5 80 cm2

140 cm3 4cm .............................. .................................

900 cm3 5 cm .............................. ..................................

1400 cm3 10 cm .............................. ..................................

28' my; oelafjk tla tla Rcq m%siauj,g wod<j W;a;r imhkak'

i. iup;=ri% Rcq m%siauhl mßudj 768 cm3 o" Wi 12 cm o fõ'(a) m%siaufha yrialv j¾.M,h fidhkak'(b) m%siaufha yrialv me;a;l È. fidhkak'

ii. RcqfldaKS ;%sfldaK m%siauhl mßudj 120 cm3 fõ'(a) m%siaufha È. 10 cm kï yrialv j¾.M,h fidhkak'(b) yrialv" RcqfldaKh wvx.= tla mdohla 6 cm kï wfkla mdofha È.

fidhkak'

iii. RcqfldaKdi% m%siauhl mßudj 960 cm3 fõ ' tys Wi 12 cm kï"(a) m%siaufha yrialv j¾.M,h fidhkak'(b) yrialv È. 10 cm kï m<, fidhkak'



mßudjwkdjrK mÍlaIKh

W;a;r yd Wmfoia

1' ;, rEmhls >kjia;=jls>klh>kldNhRcqfldaKdi%hjD;a;his,skavrhf.da,hiudka;rdi%h;%sfldaKh

2'.fvd,a leghlvodishfnda,hud¿ áka tlúiaflda;= fmÜáhíf,aâ ;,hfmd;ulk lE,a,

3. i. ivii. v.iii. vi.

4. i. 1cm ii. 2cm iii. 3cm5.

i. 2cm 1cm 1cmii. 3cm 1cm 2cmiii. 4cm 2cm 1cm

6. i. 2,2cm3

ii. 3,3cm3

iii. 6,6cm3

7. ii

iii. 32 2 1 4cm

iv. 35 2 1 10cm

v. 38 5 1 40cm

8. ii. 310 4 5 200cm

iii. 38 7 10 560cm

iv. 312 8 10 960cm

>klh fla;=j>kldNh ;%sfldaK m%siauhis,skavrh p;=ia;,h

È. m<, Wi

32 1 1 4cm



9. ii. 34 2 2 16m

iii. 310 5 3 150m

iv. 38 5 4 160m

v. 312 8 4 384m

10. ii. 35 5 5 125cm

iii. 310 10 10 1000cm

iv. 312 12 12 1728cm

v. 320 20 20 8000cm 11. ii.

iii.iv.v.

12. ii.iii.iv.v.vi.

13. i. 23 2 6cm

ii. 24 3 12cm

iii. 25 2 10cm

14. ii. 38 , 6 ,10 ; (8 6) 10 480cm cm cm cm

iii. 35 , 5 , 5 ; (5 5) 5 125cm cm cm cm

iv. 312 ,8 , 2 ; (8 2) 12 192cm cm cm cm

15. ii. 2 38 6 4 8 ; 4 8 1 0 4 8 0cm cm

iii. 2 35 5 2 5 ; 2 5 5 1 2 5cm cm

iv. 2 38 2 1 6 ;1 6 1 2 1 9 2cm cm

16. ii. 31 0 8 8 0 cm

iii. 32 5 3 7 5 cm

iv. 31 0 0 2 4 2 4 0 0 cm

17. ii. 36 4 2 4 m

iii. 320 12 240m

iv. 31 8 1 0 1 8 0m

18. ii. 218 6 24

2cm iii. 21

10 4 202

cm iv. 2112 5 30

2cm

19. ii. 2305122

1cm iii. 225510

2

1cm iv.. 236612

2

1cm

>kldNhiup;=ri% msrñvh;%sfldaK m%siauhfla;=jis,skavrh



20.

21. ii.iii.iv.

22. i.21

4 3 62

cm

ii.21

6 8 242

cm

iii.21

5 12 302

cm

23. i. 36 5 30cm

ii. 324 14 336cm

iii. 330 15 450cm

24. i.21

10 6 302

cm

ii.21

4 12 242

cm

iii.21

20 8 802

cm

25. i. 33 0 8 2 4 0 cm

ii. 324 10 240cm

iii. 38 0 1 2 9 6 0 cm

26. ii.120

430

cm

iii.48

412

cm

iv.220

1120

cm

27. ii.2140

354

cm

iii.2900

1805

cm

iv.21400

14010

cm

iup;=ri%RcqfldaKdi%iuoaùmdo ;%sfldaK

wjidk W;a;rhg kshñ;tall wjYH hs'



4' jD;a;hl j¾.M,h

ld¾h úYaf,aIKh

4'1 jD;a;hl ,laIK

4'2 jD;a;fha j¾.M,h

4'3 jD;a;hl j¾.M,h wdY%s; fhÿï



jD;a;hl j¾.M,hwkdjrK mÍlaIKh



4'1 jD;a;hl ,laIK1' 4'1'1 jD;a;hl wrh y÷kd .kshs'2' 4'1'2 jD;a;hl wrh § we;s wlaIrh weiqßka kï lrhs'3' 4'1'3 jD;a;hl wrh kï lr ,shd olajhs'4' 4'1'4 jD;a;hl úIalïNh yd mßêh w;r wkqmd;h ±laùug ixfla;h

fhdod .kshs'

5' 4'1'5 ys w.h 7

22 hkak Ndú; lrhs'

6' 4'1'6 ys w.h oYu ia:dk follg ksjerÈj 3'14 hkak Ndú; lrhs'

4'2 jD;a;fha j¾.M,h

7' 4'2'1 wrh r jQ jD;a;hl j¾.M,h 2r nj m%ldY lrhs'

8" 9" 4'2'2 wrh ÿka úg jD;a;fha j¾.M,h fiùug 2r hkafkys" wrfha w.h

wdfoaY lrhs'

10"11 4'2'3 wrfha w.h 2r hkafkys wdfoaY lr jD;a;fha j¾.M,h fidhhs'

12"13

14' 4'2'4 j¾.M,h ÿkaúg jD;a;fha wrh .Kkh lrhs'

4'3 jD;a;hl j¾.M,h wdY%s; fhÿï15' 4'3'1 RcqfldaKdi%hlska jD;a;hla bj;a l<úg ,efnk b;sß fldgfia

j¾.M,h .Kkh lrhs'16' 4'3'2 jD;a;hlska RcqfldaKdi%hla bj;a l< úg ,efnk b;sß fldgfia

j¾.M,h .Kkh lrhs'17' 4'3'3 RcqfldaKS iuoaùmdo ;%sfldaKhlska jD;a;hla lmd bj;a l< úg

,efnk b;sß fldgfia j¾.M,h .Kkh lrhs'18' 4'3'4 jD;a;hlska tal flakaøsl jD;a;hla bj;a l< úg ,efnk b;sß

fldgfia j¾.M,h .Kkh lrhs'19' 4'3'5 jD;a;hl j¾.M,h yd tu jD;a;fha wrh fuka fo.=Khl wrhla

iys; jD;a;hl j¾.M,h w;r wkqmd;h fidhhs'



4' jD;a;hl j¾.M,hwkdjrK mÍlaIKh

m%Yak m;%h

1' jD;a;hl wrh ±lafjk rEmh háka brla w¢kak'i.

ii.

iii.

2' jD;a;fha wrh ±lafjk bx.%Sis wlaIrh ;s;a br u; ,shkak'i.

....................

ii.

....................

iii.

....................

. . .

. . .

. . .

. a . b

. c

. x

. z

. y

. p . q

. r



3' jD;a;hl wrh ksrEmKh jk f¾Ld lKavh ;s;a br u; ,shkak 'i.

....................

ii.

....................

iii.

....................

4' jD;a;hl mrêh yd úIalïNh w;r wkqmd;h ±lafjk ixfla;h háka brlaw¢kak'

i. (a) (b) (c)

ii. (a) (b) (c)

iii. (a) (b) (c)

5' jvd;a ksjeros m%ldYh háka brla w¢kak'jD;a;hl mßêh yd úYalïNh w;r wkqmd;h jkqfha "

i. (a)7

22(b)

22

7(c)

3

22

ii. (a)3

1(b)

7

22(c)

5

22

iii. (a)6

7(b)

7

22(c)

22

7

6' jvd;a ksjeros m%ldYh háka brla w¢kak'jD;a;hl mßêh yd úIalïNh w;r wkqmd;h oYu ia:dk follg ,shQ úg w.hjkqfha "

i. (a) 3.72 (b) 3.21 (c) 3.14

ii. (a) 3.24 (b) 3.14 (c) 3.34

iii. (a) 3.17 (b) 3.61 (c) 3.14

.

A

B

.

C

D

O

. O

. A O

.

O

K . O

D

. O . O

. O

S

R

M

E

F

hs' hs' hs'

hs' hs' hs'

hs' hs' hs'

hs' hs' hs'

hs' hs' hs'

hs' hs' hs'



7' jvd;a ksjerÈ m%ldYh háka brla w¢kak'

i. wrh s jQ jD;a;hl j¾.M,h jkqfha "

(a) s2 (b) 22 s (c) 2s

ii. wrh t jQ jD;a;hl j¾.M,h jkqfha "

(a) 22 t (b) 2t (c) t

iii. wrh r jQ jD;a;hl j¾.M,h jkqfha "

(a) 2r (b) 22r (c) 22 r

8' ksjerÈ m%ldYh háka brla w¢kak'

i. wrh 6 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "

(a)26

7

22cm (b)

266 cm (c)266

7

22cm

ii. wrh 8 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "

(a) 87

22 (b) 88

7

22 (c) 888

7

22

iii. wrh 5.5 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "

(a) 5.55.57

22 (b) 25.5

7

22 (c) 5.5

7

222

9' A fldgfiys wrh § we;s jD;a;j, j¾.M," B fldgiska f;dard hdlrkak'

jD;a;fha wrh jD;a;fha j¾.M,h

r 557

22

p 337

22

3 rr 7

22

5 777

22

7 pp7

22

h' h' h'

h' h' h'

h' h' h'

hs' hs' hs'

hs' hs' hs'

hs' hs' hs'



10' ksjerÈ W;a;rh háka brla w¢kak' i. wrh 7 cm jQ jD;a;hl j¾.M,h jkqfha"

(a) 145 cm2 (b) 44 cm2 (c) 154 cm2

ii. wrh 14 cm jQ jD;a;hl j¾.M,h jkqfha"(a) 716 cm2 (b) 616 cm2 (c) 666 cm2

iii. wrh 21 cm jQ jD;a;hl j¾.M,h jkqfha"(a) 1386 cm2 (b) 1586 cm2 (c) 1366 cm2

11' ksjerÈ W;a;rh háka brla w¢kak' i. wrh 10.5 cm jQ jD;a;hl j¾.M,h jkqfha"

(a) 864.5 cm2 (b) 962.5 cm2 (c) 346.5 cm2

ii. wrh 3.5 cm jQ jD;a;hl j¾.M,h jkqfha"(a) 38.5 cm2 (b) 83.5 cm2 (c) 36.6 cm2

iii. wrh 17.5 cm jQ jD;a;hl j¾.M,h jkqfha"(a) 692.5 cm2 (b) 962.5 cm2 (c) 926.5 cm2

12' § we;s f;dr;=re wkqj j¾.M,fhka iudk rEmj, wlaIr ;s;a br u;,shkak'

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

.

a

14cm .

b

21cm .

c

14cm .

d

35 cm .

e

20 cm .

f

28 cm

h' h' h'

h' h' h'

h' h' h'

h' h' h'

h' h' h'

h' h' h'

13' § we;s f;dr;=re wkqj ta ta jD;a;hg wh;a wrh" A fldgqj ;=<ska f;dardhd lrkak'

Aj¾.M,h jD;a;fha wrh

3.5 cm

962.5 cm2 7.5 cm

346.5 cm2 10.5 cm

38.5 cm2 12.5 cm

17.5 cm



15' ksjerÈ W;a;rh háka brla w¢kak'

rEmfha ±lafjk wdldrhg RcqfldaKdi%hlskajD;a;dldr fldgila bj;alr we;'

(a) È. 25 cm yd m<, 20 cm jk RcqfldaKdi%fhka wrh 7 cm jQ jD;a;hlalmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 154 cm2 ii. 346 cm2 iii. 355 cm2

(b) È. 10 cm yd m<, 8 cm jk RcqfldaKdi%fhka wrh 3.5 cm jQ jD;a;hlalmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 80 cm2 ii. 38.5 cm2 iii. 41.5 cm2

(c) È. 30 cm yd m<, 25 cm jk RcqfldaKdi%fhka wrh 10.5 cm jQjD;a;hla lmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 346.5 cm2 ii. 403.5 cm2

iii. 750 cm2


rEmfha ±lafjk wdldrhg jD;a;hlskaiup;=ri%hla lmd bj;alr we;'

(a) wrh 10.5 cm jk jD;a;hlska" me;a;l È. 8.5 cm jk iup;=ri%hla lmdbj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 346.5 cm2 ii. 72.25 cm2 iii. 274.25 cm2

h' h' h'

h' h' h'

h' h'h'

h' h' h'

14' § we;s f;dr;=re wkqj ta ta jD;a;hg wh;a j¾.M,h " B fldgqj ;=<ska f;dardhd lrkak'

B

316 cm2

536 cm2

1386 cm2

786 cm2

154 cm2

274 cm2

. 21 cm

. 14 cm

. 7 cm



(b) wrh 7 cm jk jD;a;hlska" me;a;l È. 5 cm jk iup;=ri%hla lmd bj;a l<úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 129 cm2 ii. 25 cm2 iii. 154 cm2

(c) wrh 14 cm jk jD;a;hlska" me;a;l È. 10 cm jk iup;=ri%hla lmd bj;al< úg b;sß jk fldgfia j¾.M,h jkqfha "

i. 716 cm2 ii. 616 cm2 iii. 516 cm2


rEmfha ±lafjk wdldrfha RcqfldaKsl"iuoaùmdo ;%sfldaKhlska jD;a;hla lmdbj;afldg we;'

(a) RcqfldaKh wvx.= mdohl È. 20 cm jk iuoaùmdo RcqfldaKsl;%sfldaKhlska" wrh 3.5 cm jk jD;a;hla lmd bj;a l< úg b;sßjkfldgfia j¾.M,h jkqfha "

i. 38.5 cm2 ii. 261.5 cm2 iii. 161.5 cm2

(b) RcqfldaKh wvx.= mdohl È. 30 cm jk iuoaùmdo RcqfldaKsl;%sfldaKhlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úg b;sßjkfldgfia j¾.M,h jkqfha "

i. 256 cm2 ii. 296 cm2 iii. 746 cm2

(c) RcqfldaKh wvx.= mdohl È. 35 cm jk iuoaùmdo RcqfldaKsl;%sfldaKhlska" wrh 10.5 cm jk jD;a;hla lmd bj;a l< úg b;sßjkfldgfia j¾.M,h jkqfha "

i. 266 cm2 ii. 328 cm2 iii. 909 cm2


rEmfha ±lafjk wdldrhg talflakaøsl jD;a;folla we| " we;=<; jD;a;h lmd bj;afldg we;'

(a) wrh 17.5 cm jk jD;a;hlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úgb;sß jk fldgfia j¾.M,h jkqfha "

i. 625.5 cm2 ii. 962.5 cm2 iii. 808.5 cm2

(b) wrh 14 cm jk jD;a;hlska" wrh 10.5 cm jk jD;a;hla lmd bj;a l< úgb;sß jk fldgfia j¾.M,h jkqfha "

i. 962 cm2 ii. 870 cm2 iii. 269.5 cm2

h' h' h'

h' h' h'

h' h' h'

h' h' h'

h' h' h'

h' h' h'

h' h' h'



(c) wrh 14 cm jk jD;a;hlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úgb;sß jk fldgfia j¾.M,h jkqfha "

i. 770cm2 ii. 462 cm2 iii. 562 cm2

19' (a) wrh r jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;sjD;a;hl j¾.M,hg ork wkqmd;h jkqfha"

i. 1:1 ii. 1:2 iii. 1:4

(b) wrh 2a jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;sjD;a;hl j¾.M,hg ork wkqmd;h jkqfha"

i. 1:2 ii. 1:4 iii. 2:16

(c) wrh 3t jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;sjD;a;hl j¾.M,hg ork wkqmd;h jkqfha"

i. 1:4 ii. 1:2 iii. 3:6h' h' h'

h' h' h'

h' h' h'

h' h' h'



4' jD;a;hl j¾.M,hwkdjrK mÍlaIKhW;a;r yd Wmfoia

W;a;r Wmfoia

1. i.

. ii.

.

iii.

.

2. i.

. a

ii.

. q

a q

iii.

. z

z3. i. CO , OD ii. OM

iii. OD4. i. (b) ii. (c) iii. (a)5. i. (a) ii. (b) iii. (b)6. i. (c) ii. (b) iii. (c)7. i. (c) ii. (b) iii. (a)8. i. (c) ii. (b) iii. (a)

9. r 557

22

p 337

22

3 rr 7

22

5 777

22

7 pp7

22

10. i. (c) ii. (b) iii. (a)11. i. (c) ii. (a) iii. (b)12. a, c, f

13. 3.5 cm

962 cm2 7.5 cm346.5 cm2 10.5 cm38.5 cm2 12.5 cm

17.5 cm

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CO fyda OD fh§u m%udKj;a h'OC,MO fyda DO ;sìh yels h'



14. 21 cm 616 cm2

536 cm2

14cm 1386 cm2

786 cm2

7 cm 154 cm2

274 cm2

15. (a) ii. (b) iii. (c) ii 16. (a) iii. (b) i. (c) iii 17. (a) ii (b) ii. (c) i. 18. (a) iii. (b) iii. (c) ii. 19. (a) iii. (b) ii. (c) i.

wkdjrk mÍlaik diagnostic testsnie.lk/pdffiles/other/som measurmaths.pdf^ introduction to...

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