lts^5[
!D grnjvlhk’I6[lujc90hk’0t|ko ABCD g,njvI6hlk,g,af A, B, C F gryoj 0ufmjvo-nj AB
c]t BCF 9kdoAogryoj 0ufmjvodq’j mu,j u.9dk’ C c]t ]aflt\ugmqkj AB c]h;0ufmjvo
dqj’mulv’muj,u.9dk’ A c]t ]aflt\ugmqkj BCD lv’mvj odq’j 8afdao16gj ,af DD gryoj 0uf
mvj o-nj [AD] c]t [CD] c]h;wfhI6[lujc90hk’0t|ko ABCD D
@D grnjvlhk’glAo-nj|b’j zjkog,af A mu.j shdjvo 0t|koda[glAo-nj d gryoj ;k’lv’g,af8kj ’
dao B c]t C 16gj lAo-nj dD c]h;0ufmjvodqj’mu,j u.9dk’ C c]t ]aflt\ugmqjk AB 9kd
oAo0ufmjvodqj’mu,j u.9dk’ A c]t ]aflt\ugmqkj BC lv’mvj odqj’8afdao16gj ,af DD
l5fmhkpgryjo0ufglAo-nj AD muj0t|koda[ dD
dyf9tdemu & X dkooe.-h;q’;Po c]t [aomafgrnvj lhk’glAo-nj8A’lkddao?
!D 9qj’;k’g,af M 16jovdglAo-nj dD c]h;.-h[aomaf c]t ;q’;Pogrnjv0ufglAo-njzjko M
c]t 8A’lkdda[ d 3fpxt8y[af8k,0Ao8vo8+wxoUG
dD
ສະຫງສ.ວວນ.ລິສຂະສິດ
d
M
M
0D
d
97
7D M
d
@ D9qj’0ufglAo-n8j A’lkdda[ d zkj o A 1j6I6[]5j,oU.
d
A
lts^5[ ສະຫງສ.ວວນ.ລິສຂະສິດ
grnjvc8h,glAo-n|j bj’zkj og,af M muj.shdvj o8A’lkdda[glAo-nj d muj.shdvj oD gryoj c8h,
mjvodq’j mu,j u.9dk’c,oj g,af M muj.shdjvooAoD mjvodq’j wx8af d 16lj v’g,af A c]t BD
c]h;gryoj c8h,lv’mjvodqj’mu,u.9dk’c,oj A c]t B c]t ,u]aflt\ufP;daoD
lv’mjvodq’j 8afdao16gj ,af M c]t vudg,af|bj’167j qo]tg[Nv’mP[da[ d c]h;0ufglAo
-njzkj o M c]t zjkog,af8afdao0v’lv’mjvodq’j oAo -bj’gxaoglAo-nj8A’lkdda[ d D
\kpgsfG glAo-nmj uwj fhoAowx8A’lkdda[ d 16gj ,afg7y’j dk’0v’ A c]t BD
dyf9tde * Xdkolhk’glAo-n8j A’lkdfh;p;ymuvnoj ?
16sj hv’ ,!/d 76wfh.shoadIPoc8h,glAo-n8j A’lkdda[glAo-nj d zjkog,af C .o0v[g9hpmuj
.shfaj’I6[]5j,oUD [a’gvuo mhk; 7e,u ]n,[aomaflkd ,uc8j[aomaf c]t ;q’;PoD
C
B
A
d
dD mhk; 7e,u ]k;.-h;ymu0hk’gmy’wfh[+L 4hk;kj [+wfh]v’7yfg[yj’;kj ]k;9tgIaf;ymu.f L
98
ສະຫງສ.ວວນ.ລິສຂະສິດ0D 9q’j c8h,glAo-nj8A’lkdda[glAo-nj d zkj og,af C 3fpxt8y[af8k,7ecotoe]5j,oUG
{ ;k’g,af A c]t B 16jglAo-nj d c]h;0ufmvj odqj’ muj,u.9dk’ A c]t ]aflt\u AC.
{ 0ufmjvodqj’ mulv’muj,u.9dk’ B c]t ]aflt\u BCD lv’mjvodqj’8afdao16gj ,af C c]t
D. l5fmhkp]k;0ufgloA -njj (CD).
D
7D 9qj’.-h[aomaflkd,kd;fg[yj’;jkglAo-nj (CD) 8A’lkdda[ d s^n [+ L
@D [qfg/ydsaf
!D 9qj’c8h,I6[lk,c9 ABC lkd16j A, I6h;jk AB = 3 cm c]t BC = 4 cm. c]h;;af
cmd];’pk; AC.
@D9qj’c8h,I6[7k’\6lkd ABCD (lkd16j A c]t D?F I6h;jk AB = 3cm, CD = 4,5cm
c]t AD = 3,8 cm.
99
#D9q’j \kpg,af A, B c]t C [+]Po-nj16jglAo-nj dD .shlhk’glAo-nj8A’lkdda[ d zkj o A, B
c]t C. la’gdfgsaoco;.fL
$D9q’j lhk’I6[lucj 9lkd ABCD mu,j u0hk’gmqjk 4 cm c]t glAogoa’j 9v,gmqkj 5 cm.
&D9q’j lhk’I6[lucj 90hk’0t|komu,j uglAogoa’j 9v,gmqkj 6cm c]t ];’pk;gmqkj lv’lj;o
lk,0v’glAogoaj’9v,D
*D9q’j \kpg,af A c]t B .lgj lAo-n|j bj’3fp;kj AB = 4 cmD ,uma’\qf9adg,afmu1j 6jsjk’ 3cm
9kd A c]t 7cm 9kd B L
(D9q’j la’gdflv’glAo-nj d c]t d’ mu1j 6.j o0v[I6[D r;d,ao9twx8afdao16sj kj ’9kd0v[
I6[s^kpxko.f X[+.sh0uf8+vvdwx9kd0v[I6[?L
d
d’ ສະຫງສ.ວວນ.ລິສຂະສິດ
le]a[0=h ( vkf9t.-h7;k,lk,kf g]njvoglAo-nj
,kdE-hkp s^n mq[l;j o mu1j 6oj vd0v[.sh,k16dj E
-hkp c]h; ;afcmd s^n 7yfw]jvkfg\ktda[zj6gdaj’
)D9qj’la’gdfI6[]5,j oU c]h;9af]Po0Ao8vodkoc8h,I6[8k,]efa[.sh4nd8hv’D
dD 0ufglAo-nzj jko K c]t 8A’lkdda[ (DC). B
0D;k’lujg,af A, B, C, D. T
7D glAo-njoAo8af XBC) 1j6 T. A C
’D 0ufglAo-nzj kj o L c]t 0t|koda[ (DB). K
9D mjvo-nj AC c]t BD 8afdao1j6g,af k L
lD glAo-njoAo8af (DC) 16j L.
-D 0ufmvj o-nj AC c]t BD. D
100
ສະຫງສ.ວວນ.ລິສຂະສິດ[qfmu !$ dko[;d];’pk;mvj o-nj c]t dko76o9eo;o.f|bj’
da[];’pk;0v’mvj o-nj
!D dyf9tde
dyf9tdemu ! Xdko[;d];’pk;mvj o-nj?
mjvo-nj AB g-y’j gIqklaopt]ad DDDDDDDDDD c,joDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
!D 9q’j xP[mP[];’pk;lv’mjvo-nXj I6[ !? c]t XI6[ @? ]5,j oUfh;plkp8k c]h;d;f
g[yj’fh;pdko;afcmdD
XI6[!? XI6[ @?
@D 9q’j xP[mP[];’pk;0v’mjvo-nj ! c]t @ fh;plkp8k c]h;d;f7nofh;pdko
;afcmdD
1
2
#D .shg,af A c]t B 16jglAo-nj dF c]h;;k’g,af M .l]j ts;jk’g,af A c]t B faj’I6[
]5j,oUD d
B
M
A
gIqkwfh @ mvj o-nj.\j DDDDDDDDDDDDc]t DDDDDDDDDDDDDDDDD gIqklk,kf0Po];’pk; AB 8k,
];’pk;0v’ @ mvj o-njmuwj fhoAo1kj ’.f L
AB = ……….. + ……….
101
4hk;jk M 1j6g7yj’dk’0v’ [AB] lv’mvj o-njoAo9tgxaoco;.fL
………. = …………
AB = …. × AM = … ×………
$D 9q’j c8h,mjvo-nj [CD] 16oj vd dF c]h;;k’g,af E 16jlj;o0uf8+[AB] gmy’glAo-nj d
3fp;jkG BE = CD. .shgvqk [CD] ,k;k’g8a’ [BE]D gIqklk,kfdeoqf
AE = …….. … ………
D ສະຫງສ.ວວນ.ລິສຂະສິດ
C
A B E
dyf9tdemu @ Xdko76o];’pk;mvj o-jnda[9eo;o.f|bj’?
!D 9q’j .-h;q’;Poc8h,mjvo-nj AE 7no3fpcmdgvqk];’pk;mvj o-nj [CD] c]h;,k\kp
.ljg7yj’glAo-nj [Ax) .shwfh AE = 3CD.
D
C
A
102
@D 9q’j c8h,mjvo-nj MN = 4,5 AB 7no3fpoe.-h;q’;PoD
M
M xa[0k;q’;Pog0Qk.sh4nd8hv’ N
H
A B
#D 9qj’c8h,mjvo-nj EF = 3 AB 7no3fpoe.-h;q’;PoD
4
A B
ສະຫງສ.ວວນ.ລິສຂະສິດ
E F
$D 9q’j c8h,mvj o-nj GH = 3× 3 PQ 7no3fpoe.-h;q’;Po.
4
P Q
3
4 PQ
G
3
3 × 4 PQ
103
ສະຫງສ.ວວນ.ລິສຂະສິດ@D .97;k,
{ 4hk;kj lk,g,af A, B c]t C 16gj lAo-njfP;dao8k,]efa[F gryoj lk,kfdeoqf
zqo[;d];’pk;0v’lv’mvj o-nj [AB] c]t [BC] fa’j oUG
AC = AB + BC
{ gryjo76o];’pk;mvj o-nj AB da[ k fh;pdkooe.-h;q’;Pogrjnvgvqk];’pk;
faj’dkj ;,k8+.ldj ao8k,glAo-nj k gmnjvD
8q;1jk’G
!D .sh AB = 6,7 cm, BC = 4,6 cm. 9q’j 7yfw]]j ;’pk; AC I6h;kj A, B c]t C 16jglAo-nj
fP;daoD
[qfcdhG gIqk,u AC = AB + BC Xgrkt A, B c]t C 16jglAo-njfP;dao8k,]efa[?F
gIqkcmo7jkwfhG
AC = 6,7 cm + 4,6 cm = 11,3 cm.
@D .o]t[q[dko;afcmdvkg,]ydk gryoj .-h 25fgxaosq;|j;p;afcmd];’pk;D
! 25f(foot) = !@ oU;X inches)F 4hk;kj AB = 18 oU;F CD = 1,5 25f
X]kp]tvPf9tltg|u.o[qf8+wx?D 9q’j xP[mP[];’pk; AB c]t CD.
[qfcdhG gIqkxjPo CD = 1,5 25f gxaooU; wfh CD = 1,5 25f ×!@ = 18 oU;
gIqklts^5[wfh;kj AB = CD.
#D .shg,af M 16j mvj o-n j AB. 9qj’-vdsk];’pk; MB Ih6;kj AM = 5 sq;|;j p c]t
AB = 8 sq;|;j pD
& sq;|;j p
A M B
) sq;|j;p
[qfcdhG phvo;kj A, M c]t B 16jglAo-nfj P;dao 8k,]efa[ gIqk,uG AB = AM + MB,
ltoAo MB = AB – AM
gIqkcmo7kj wfhG MB = ) sq;|;j p – & sq;|j;p = # sq;|;j pD
104
#D [qfg/ydsaf
!D 9q’j ;k’g,af K 16jmjvo-nj MNF c]h;-vdsk];’pk; KN I6h;kj G MN = 9,35 cm c]t
MK = 5,6 cm.
N
M
@D .shg,af A, B, C, D, E c]t F 16jglAo-nj d 3fp;jk AB = CD = DE = 2,8 cm,
AF = 10,2 cm; BC = EF. 9q’j -vdsk];’pk; BC.
d
#D 9q’j -vdsk];’pk; NP 8k,I6[mu,j u0=h,6o]5j,oU G ສະຫງສ.ວວນ.ລິສຂະສິດ
MN = PQ = QR
9cm
M N P Q R
2,6cm
$D 9qj’xP[mP[];’pk;0v’glAomk’ AEFGHIJB c]t AMB fh;plkp8k
X3fp[+.sh7yfw]?j G H
F I
E J
M
A B
c]h;.sh7yfw]zj qo[;d0v’];’pk;mjvo-nj [AE], [EF], [FG], [GH], [HI], [IJ] c]t
[JB]F c]t zqo[;d];’pk;0v’ [AM] c]t [MB]. c]h;d;fg[y’j 7e8v[
0hk’gmy’D
105
&D 9q’j la’gdfI6[]5,j oU c]h;[vd;kj glAomk’.flAod;kj F glAomk’ A s^n glAomk’ B?
A B
*D 9q’j 7kf7tgofh;plkp8k ;jk];’pk;0v’glAosad16]j 5j,oU |hvpd;jk s^n s^kpd;jk
15 cm.
(D9qj’xP[mP[];’pk;glAosad I6[ ! c]t ];’Iv[0v’I6[ @ fh;plkp8k F c]h;
d;f7nofh;pdko;afcmdD
7,2 sq;|j;p
I6[ @
ສະຫງສ.ວວນ.ລິສຂະສິດ
I6[!
)D 9qj’-vdsk];’Iv[0v’c8j]tI6[]5j,oU 8k,0=h,6omu.j sh.
10,3 sq;|j;p 7 sq;|j;p 6 sq;|;j p
106
_D 9qj’-vdsk];’Iv[0v’I6[fyol;o]5j,oUX.shsq;|;jp8q;9y’gxao hm)
2,5 1,5
3,5
4,5
7,5
!WD 9q’j c8h,mvj o-nj AB c]h;c8h,G
{ mvj o-nj muj,u];’pk;gmqjk 5 AB
{ mjvo-nj mu,j u];’pk;gmqkj 3
5 AB
{ mvj o-njmuj,u];’pk;gmqkj 5 3 ABX5 3 3
4 4 = 5 + 4 ).
!!D dD 9q’j c8h,mjvo-nj AB muj ,u];’pk;gmqjk 6 cm. ສະຫງສ.ວວນ.ລິສຂະສິດ
0D c8h,mvj o-nj mu,j u];’pk;gmqkj 4
3 AB;
7D c8h,mvj o-nj muj,u];’pk;gmqkj 3
2 AB.
!@D9q’j c8h,mjvo-nj MP muj,u];’pk;gmqjk 7,6 cm. c]h;\kpg,afg7yj’dk’ N 0v’
mjvo-nfj aj’dkj ;D
9q’j [vd];’pk;0v’ NP. c]h;8nj,.l[j jvo9Eg,afgrnjv.shgxaoxt3spd3fpoe.-h
7e;jk “ gxaog7y’j |b’j ” s^n “gxaolv’gmnjv” G
MN……………. 0v’ MP ; MP…………………..0v’ NP
MP…………….. 0v’ MN ; NP…………………...0v’ MP.
!#D 9qj’c8h,mjvo-n j AB c]h;oe.-h[aomaf c]t ;q’;Pogrnjvc8h,mvj o-nj BC XA, B c]t C
[+]Po-n?j muj,u];’pk;gmqkj lv’gmnjv];’pk;0v’ ABD 9kdoAo.shc8h,mvj o-nj CD
mu,j u];’pk;gmqjklk,gmnjv];’pk;0v’AB (B, C c]t D [+]Po-nj?
107
ສະຫງສ.ວວນ.ລິສຂະສິດ[qfmu !& dko;afcmd];’pk;0v’mjvo-nj
!D dyf9tde
dyf9edemu !D
dko;afcmd];’pk;c,jodkoxP[mP[];’pk;oAo.ljsq;\;j p;afcmdmujg]nvdw;hD
sq;|j;p.odko;afcmd];’pk;c,oj G c,af (rklk/^aj’G mètre; rklkva’dyfG metre
s^n meter) g-yj’gmqkj da[|bj’lj;oly[]hko0v’|bj’lj;oluj0v’glAoc;’X!W WWW km?
g-yj’gxaoglAoIv[|;j p3]dmujzjkoma’lv’0;Ao3]d Xg[yj’I6[?D
dD grnjv;afcmd];’pk;muj|hvpd;kj c,af gryoj gIafco;.fL
gryoj .-hc,af;afcmdlyj’mu,j u];’pk; |hvpd;kj ! c,afwfh s^n [+L 4hk;jk[+gryoj
cdhw01jk’.f L
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
gryjo[+lk,kf.-h c,afgrnjv;afcmd];’pk;muj|hvpd;kj ! c,afwfhD
ltoAogryoj 9b’j c[’j ! c,afvvdgxao !W l;j ogmqkj daoD c8j]tl;j ogvUo;kj
108
! gf-uc,af Xdm sp=h,k9kd decimeter).
0 1 2 3 4 5 6 7 8 9 10
I6[0v’w,hc,afsp=h];’pk;]q’ !W gmnvj X,kf8kl;j o ! G !W?
w]ptskj ’]ts;jk’lv’0ufltcf’g4y’ ! gf-uc,af g-y’j sp=h ! c,af]q’ !W gmnvj D
! dm = 1 m = 0,1 m; s^n 1 m = 10 dm
10
0D grnvj ;afcmd];’pk;muj|hvpd;kj ! gf-uc,afgryjogIafco;.fL
gryjoc[’j ! gf-uc,afvvdgxao !W lj;ogmqkj daoD c8]j tl;j ogvUo;kj ! -a’8uc,af
(cm, sp=h,k9kd centimeter)D
1 cm = 1 dm=0,1 dm s^n 1 dm = 10 cm ສະຫງສ.ວວນ.ລິສຂະສິດ
10
1cm
1dm
g-ajofP;dao grnvj ;afcmd];’pk;|hvpd;jk ! -a’8uc,af gryjoc[’j
-a’8uc,afvvdgxao !W lj;ogmqkj dao c8j]tl;j ogvUo;kj ! ,yo]uc,af (mm, sp=h,k9kd
millimeter) 1cm
1 mm = 1 cm = 0,1 cm s^n 1cm =10 mm
10
1mm
109
dyf9edemu @ D
dD 9qj’;afcmdmjvo-nj]5,j oU c]h;gvqk7jk;afcmd8n,j .l8j k8t]k’D
F
E
A
C
D
B H
I G
mjvo-nj ];’pk;16j]ts;jk’ J
…..cm c]tDDDDDDDDcm
AB 5 cm c]t 6 cm ];’pk;cmdgxao mm
CD 3 cm c]t 4 cm
EF 52 mm
33,3 mm
ສະຫງສ.ວວນ.ລິສຂະສິດ
GH
IJ
0D 9q’j c8h,mjvo-ngj -y’j ];’pk;wfhdeoqfw;h16j8k8t]k’]5j,oUG
mvj o-nj ];’pk; mjvo-nj ];’pk;16j]ts;jk’
DDDDDDDDDDDDDDDD c]t DDDDDDD
AB 5 cm KL 0,8 dm c]t 0,9 dm
CD 145 mm MN 4,6 cm c]t 5,7 cm
EF 4,5 cm PQ 0 dm c]t 0,8 dm
GH 0,8 dm RS 56 mm c]t 57 mm
IJ 38 mm TU 6 cm c]t 7cm
110
8q;1jk’D B
5 cm
A 0,8 dm < KL<0,9 dm
K L
\kpgsfG le]a[]t[q[vkg,]ydk gryjo.-h25f Xmt;u76o c]t v5xt76o0v’25f?
gxaosq;|j;p ;afcmd];’pk;D
! 25f(foot) = 12 oU; Xvyo-% inches)
! 1kf(yard) = 3 25f = 0,9144 c,af
@D .97;k,
dD sq;|j;p;afcmd];’pk;
ສະຫງສ.ວວນ.ລິສຂະສິດ
sq;|j;p;afcmd];’pk;c,oj G c,afF v5xt76o c]t mt;u76o0v’c,afD
gf-uc,af Xdm), -a’8uc,af (cm) c]t ,yo]uc,af (mm) gxao v5xt76o0v’c,af (m)D
gfdkc,af (dam), gIad38c,af(hm) c]t dy3]c,af(km) gxao mt;u76o0v’ c,af(m)D
1 dam = 10 m; 1 hm = 10 dam; 1 km = 10 hm
8hv’9nGj
1 km = 10 hm 1 m = 10 dm
1 hm = 10 dam 1 dm = 10 cm
1dam = 10 m 1 cm = 10 mm
1 km = 1 000 m 1 m = 100 cm
1 hm = 100 m 1 m = 1 000 mm
1 m = 0,001 km 1 mm = 0,001 m
1 m = 0, 01 hm 1 cm = 0,01m
1 m = 0,1 dam 1 dm = 0,1 m
111
0D dkoxPj osq;|;j p;afcmd
dkoxjPosq;|;j p,ulv’;ymuG
;ymumu ! dkooe.-h8k8t]k’
grnvj 7;k,ltf;d.odkoxjPosq;|;j pgryjogvqksq;|;j pfa’j dkj ;.l.j o8k8t]k’fa’j oUG
×1000
×100
×10
km hm dam m dm cm mm
÷10
8q;1jk’G ÷100
xjPo 74,5703 dam gxao cm: ÷1 000
gIqkla’gdfgsao;jk 4 gxao8q;g]dsq;|j;p0v’ 74,5703 dam. gIqk;k’,ao.l4j ao dam
ສະຫງສ.ວວນ.ລິສຂະສິດ
9kdoAo gIqkgvqk 8q;g]dc8]j t8q;]q’.l8j k,c8j]tsq;|;j pmujdq’daoD
gIqkphkp95fwx.lj4ao cm: 74,5703 dam = 745 7,03 cm
km hm dam m dm cm mm
7 4 5 7 0 3
1 0 0 0
1 0 0
1 0 0 0
0 0 1
0 0 0 1
le]a[8q;1jk’]5,j oU gryjod=xt8y8k,;y[af;ymufP;daoG
xjPo 1km gxao m; xPj o 1m gxao km,
xPj o m gxao cm; xPj o 1cm gxao m;
xjPo m gxao mm; xjPo 1 mm gxao m D
7e8v[G
1 km = 1 000 m 1 m = 0,001 km
1 m = 100 cm 1 cm = 0,01 m
1m = 1 000 mm 1 mm = 0,001 m
112
;ymumu @
gryjo76o s^n sko.sh !WF !WWF !WWWF D D D
8q;1kj ’ D 9qj’xjPo 3,4 km gxao m, c]h;xjPo 250 m gxao hm.
× 1 000
÷100
km =
3,4 km = 3 400 m
m m = hm
250 m = 2,5 hm
#D [qfg/ydsaf
!D 9qj’\k[g,af A, B, C, c]t D 8k,]efa[.lgj lAo-nj d 3fp;jk AB = 7,4 cm:
CD = 0,3 dm; AD = 125 dmF c]h;-vdsk BC gxao dam.
100
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9q’j xjPo9e8+wxoUgxao c,af (m), gf-uc,af(dm), -a’8uc,af(cm) c]t ,yo]uc,af(mm)G
dD 5 hm 40 dam 3 m; 0D 25 m12 cm 7 mm;
7D 1,2 km 5 dam 13 m; ’D 139,5 hm;
9D 2 dm 13 cm; lD 28,016 km;
-D 7m 1,3 dm 7 mm; pD 0,07103 dam.
#D 9q’j 8n,j 8q;g]d s^n sq;|j;p;afcmd];’pk;mujg\ktlq,.l[j vj o9Eg,afG
dD 3,7 m = .... cm 0D 52 cm = 0,052….
7D 12,4 hm 07 dam = …m; ’. 205 m = 0,205….
9D 712 mm = …….dm lD 5,74 dam = 5740…..
-D 3 m = …..mm pD 25 dam 08 cm = … … m
100
$D 9qj’xP[mP[];’pk;]5j,oUG 0D 10 000 dm c]t 10,1 km
dD 518,03 cm c]t 51,31dm; ’D 2,01 hm c]t 30,1 m
7D 453,7 dm c]t 4,5 dam ;
113
&D 9q’j xjPo];’pk;8+wxgxao,yo]uc,af Xmm):
dD 15 cm; 1 cm; 12,7 cm; 0,35 cm
0D 21 m; 0,27 m; 0,0019 m; 5,0014 m.
7D 4 dm; 1,72 dm; 0,365 m; 0,6501 dm.
*D 9qj’xjPo];’pk;8+wxgxao-a’8uc,af(cm):
dD 1 400 mm; 100 mm; 0,1 mm; 1 219 mm.
0D 9 dm; 0,001 dm; 3,104 dm; 0,00347 dm.
(D 9q’j xjPo];’pk;8+wxoUgxaody3]c,af (km):
dD 26 790 m; 3 087 m; 102 m; 42 m.
0D 420 dam; 32,49 dam; 398,002 dam; 23,1 hm; 0,54 hm.
)D 9q’j 7yfw]fj h;plv’;ymu8jk’daoG
dD 875m × 3 S 0D 2943cm×7 S 7D 235,718cm × 7
5 9 11
ສະຫງສ.ວວນ.ລິສຂະສິດ
XcotoeG ;ymu ! 0Po 875 = 175x5 c]h;xt8y[afdkoIvo?
_D dD grnjvgIaf\a’lnzjkocfo dt-;’8jk’xtgmfwfhcotoe.shxtdv[7eIhv’7af8yfwx
fh;pI6[ 4x6, gryoj \kp7;k,;jkgryjo .-hvao.fgxaosq;|;j p 0v’0t|kfI6[ L
0D 16jIhko0kpg7nvj ’o5’j gryjowfh8yfg]d ## .llj ;j ocv;0v’3lh’D gryoj \kp7;k,;jk
## sq;|j;pvao.f L
!WD ’6 @W ;kg0QkI6,N]tlvd vvdI6,N]t7n[D 4k,;jk9ad,N,ao9b’j g0QkI6s;yfL
X! ;k = $ lvdS ! lvd = @F& 7n[?
!!D ok’ ok]u ,uvkp5gmqkj @ gmnjvvkp50v’ok’ ]yofkD mhk; mv’ ,uvkp5]jon ok’ ok]u
!& xu c]t ]njo mhk; 7e @W xuD ma’ $ 7qo,uvkp5];,dao !(W xuD
dD 9q’j c8h,mjvo-nlj tcf’g4y’vkp5c8]j t7qoX gvqk0=h,6oc8j]t7qo]q’.lIj 6[?D
0D -vdskvkp50v’]yofk c]h;-vdskvkp5zh6vnoj MD
vkp50v’ ok]u
vkp50v’ ]yofk DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
114
ສະຫງສ.ວວນ.ລິສຂະສິດ!@D mhk; lad ,uvkp5gmqjklv’gmnvj vkp50v’mhk; [5o g-yj’gxaorujohv’fP;daoD mhk; [5o vjvo
d;jk ok’ [q;lu mugj xaogvNvp0v’]k; * xuD r;dg0qkma’lk,,uvkp5];,daogmqkj da[
vkp5c,8j h60v’ r;dg0qkG )@ xuD
dD 9qj’c8h,mjvo-njltcf’g4y’vkp50v’ma’lk,7qoS
0D 9q’j -vdskvkp50v’mhk;ladS
7D 9q’j -vdskvkp50v’ok’ [q;lu c]t mhk;[5oD
!#D dD 9q’j c8h,I6[|hk8+wxoU7noS
0D 9q’j ;afcmd0hk’ c]t glAogoa’j 9v,D
!$D 16gj 9hpmu,j u8kdk3iG
dD 9qj’c8h,mvj o-nj AB muj,u];’pk;gmqjk ) 8kdk3iS c]h;c8h, mvj o-nj mu,j u];’pk;
gmqkj $ 8kdk3ig7yj’ c]tmvj o-nj muj,u];’pk;gmqjk * dk3iS
0D 9q’j ;afcmd];’pk; AB, CD c]t EF gxao,yo]uc,af(mm )S
7D 9qj’;afcmd];’pk;8kdk3ivao|bj’ c]h;7yfw]sj k];’pk; AB, CD c]t EF.
XxP[mP[zqomujwfhIa[da[zqo0v’0=h 0?D
!&D 9qj’c8h,I6[lk,c9 ABC lkd16j A I6h;jk AB = 3 cm c]t BC = 4 cm c]h;afcmd
];’pk; AC.
16. 9q’j c8h,I6[7k’\6lkd ABCD(lkd16j A c]t D ?, I6h;jk AB = 3 cm, CD = 4,5 cm c]t
AD = 3,8 cm.
!(D .shg,af A, B c]t C [+]Po-n1j 6jglAo-nj dD 9qj’lhk’glAo-nj 8A’lkdda[ d zkj o A, B c]t C.
la’gdfgsaoco;.fL
!)D 9qj’lhk’I6[lujc9lkd ABCD mu,j u0hk’gmqkj 4 cm c]t glAogoa’j 9v,gmqkj 5 cm.
115
[qfmu !* dko;afcmd];’pk;
!D dyf9tde
dyf9tdemu !G v5xtdvo;afcmd];’pk;
dD v5xtdvomugj ryjo.-hgrnvj ;afcmd];’pk;,uspa’cfjL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
0D .oltw\dvj o s^n 16gj 0fsjk’wdlvds^udmju[+,uv5xtdvo;afcmd];’pk; gryjo.-hspa’
grnjv;afcmdL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
v5xtdvo;afcmd];’pk;
I6[ ! ສະຫງສ.ວວນ.ລິສຂະສິດ
I6[ &
I6[ @ I6[ *
I6[ #
I6[ (
I6[ $ I6[ )
116
7D 9qj’0Po8nj,8k8t]k’]5,j oUG
]}f lyj’mu;j afcmd v5xtdvo.-h;afcmdmujg\ktlq,
! 0t|kf0v’dtfko w,hc,af
@ ];’pk;vk7ko3I’IPo
# ];’pk;F ];’d;hk’ 0v’mqj’ok
$ ]aflt\u0v’glAozq,
& 0t|kf0v’c[dg8gip
* Iv[cv;
( ];’pk;czoj cr
) ];’pk;0v’glAo37h’
_ glAozjko.9dk’]6d7ezkp
dyf9tdemu @ D ສະຫງສ.ວວນ.ລິສຂະສິດ
9qj’lhk’I6[lk,c9 ABC; Ih6;kj AB = 6 cm; AC = 4 cm; BC= 3cm. 3fp.shxt8y[af8k,
0Ao8vo]5,j oUG
{ c8h,mjvo-nj AB = 6 cm;
A B
{ 0ufmvj odq’j muj,u.9dk’ A c]t ]afl\u gmqjk AC ;
117
{ 0ufmvj odqj’0v’;q’,qomu,u.9dk’ B c]t ]aflt\ugmqkj BC. ສະຫງສ.ວວນ.ລິສຂະສິດ
c]h;0ufmjvo-nj AC c]t BC
dyf9tdemu #
dD 9q’j la’gdfI6[w,h[aomaf]5,j oU c]h;8v[7e4k,DD
0 1 2 3 4 5 6 7 8 9 10
I6[0v’w,hc,afsp=h]q’ !W gmnvj X,kf8kl;j o ! G !W?
{ 16j.oI6[w,h[aomaf,uma’\qf9ad0uf L
{ ,uma’\qf9ads;kj ’X[+oa[lv’s;kj ’ohvp1j6lv’lQo?L
{ 9q’j xP[mP[9eo;os;kj ’da[9eo;o0ufma’\qf c]h;0Po8nj,.l[j vj o9eg,afD
9eo;o0uf = DDDDDDDDDD
9eo;os;jk’ = DDDDDDDDDD
9eo;o0uf = 9eo;os;jk’ + D D D D = D D D D + D D D D
118
ສະຫງສ.ວວນ.ລິສຂະສິດ0D 9q’j la’gdfI6[]5,j oU c]h;0Po8n,j .l[j jvo9Eg,afD
A B
16j]ts;kj ’ A c]t B ,uma’\qf9ad0uf L D D D
,uma’\qf9ads;kj ’L D D D
7D 9qj’la’gdfI6[]5,j oUD
oa[9kd A wxmk’g[Nv’0;k,n ,uma’\qf9ad0ufL c]t ,uma’\qf9ads;jk’L
9q’j .sh0=hlts^5[3fp0Po8nj,.l[j vj o9Eg,afD
A
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
’D 9qj’la’gdfc8j]tI6[]5,j oU ,uma’\qf9adg,af L c]t ,uma’\qf9ads;jk’L 9qj’.sh0=h
lts^5[3fp0Po8nj,.lj[vj o9Eg,afD
I6[ ! I6[ @
16jI6[ ! ,uma’\qfDDDDDDDDDDDDDDDDDDg,af c]t ,uma’\qfDDDDDDDDDDDDDDDDDDDs;jk’D
16jI6[ @ ,uma’\qfDDDDDDDDDDDDDDDDDDg,af c]t ,uma’\qfDDDDDDDDDDDDDDDDDDDs;kj ’D
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
dyf9tdemu $
!D 9q’j xP[mP[];’Iv[0v’lv’I6[]5,j oU Xfh;plkp8k c]h;d;ffh;pg7nvj ’,n?
4hkgIqk.shI6[gs^qjkoU8yf.oI6[9t85]af
9tlk,kfxP[mP[wfh]aflt\u0v’
;q’,qo c]t mjvodqj’K
I6[ ! I6[ @
119
@D 9qj’-vdsk];’Iv[0v’I6[8+wxoUD
1cm 5 cm
9 cm
cotoeG { g7jy’;q’,qoc8]j tvao,u];’pk;gmqjkdaoD
{ ];’Iv[0v’;q’,qogmqjk 2π r X r c,jo]aflt\u?
#D 9qj’-vdsk];’Iv[0v’I6[]j5,oUD ສະຫງສ.ວວນ.ລິສຂະສິດ
6,35 cm
3,02 cm
3,65 cm
1 cm
2 cm
$D I6[lujc9lkd]5j,oUwfhlhk’0Bo3fpdko0uf8+I6[9t85]af-b’j ,u0hk’gmqjk !W sq;|j;pD
9q’j la’gdfg[y’j ];’d;hk’ c]t ];’pk;0v’I6[ lujc9lkdfa’j dkj ; c]h;-vdsk];’
Iv[0v’,aoD
!W sq;|;j p
120
ສະຫງສ.ວວນ.ລິສຂະສິດ@D .97;k,
dD v5xtdvo;afcmd];’pk;
7qoltw\dvj o s^n -k;[hkomuj[+,uv5xtdvo;afcmd];’pk; gryjo,ad.-Gh ;kF lvdF
8uoF 7n[ s^n oU; XoU;3xh? grnvj ;afcmdD
ltw|xt95[aogryjo.-hG w,hc,afF c,afd=h3]F c,afd=hzhkF dhv’95]tmafF c,afra[F
[aomafXf6[gf-uc,afX@W cm?F g7nvj ’;afcmdI6[-q’dq,F c]tvnoj MDDDDDDDDDDDDD
0D w]ptsjk’
4hk;kj ,u0uf16jlv’lQo F 9eo;o0uf = 9eo;os;kj ’ + !
4hk;jk[+,u0uf16lj v’lQo F 9eo;o0uf = 9eo;os;jk’ − !
4hk;kj ,u0uf16lj QofP; F 9eo;o0uf = 9eo;os;jk’
d=]touglAo;q’9vovaf F 9eo;o0uf = 9eo;os;jk’
8q;1kj ’ D
16jc7,4t|qocsj’|b’j Xlq,,5f;kj -nj? gryoj x6d8Qow,h lv’8Qo.fsjk’dao & c,afD
];’pk;0v’4t|qogmqjk @ dy3]c,af. Ih6;kj 16lj v’lQo[+,u8Qow,h?
dD 9q’j xP[mP[9eo;o8Qow,h c]t 9eo;os;kj ’S
0D 9q’j -vdsk9eo;o8Qow,hma’\qfD
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
[qfcdhG
xjPo 2 km gxao 2 000 m
9eo;os;jk’G 2 000 m ÷ 5 m = 400 s;kj ’
phvo;kj [+,u8Qow,h16lj v’lQo 9eo;os;kj ’ = 9eo;o8Qow,h + ! s^n
9eo;o8Qow,h = 9eo;os;jk’ – 1 = 400 – 1= 399 8QoD
121
7D dko-vdsk];’Iv[
dko-vdsk];’Iv[,u @ ;ymuG
!D le]a[I6[s^kpc9 gryoj [;d];’pk;0v’0hk’D
@! sq;|j;p D
8q;1jk’D !WF& sq;|j;p
C
A
AB = 5 sq;|j;pS B
BC = 11 sq; |;j p
CD = 10,5 sq;|j;p & sq;|j;p
!! sq;|;j p
AD = 21 sq; |j;p
];’Iv[ = ( 5 + 11 + 10,5 +21 )sq;|;j p = 47,5 sq;|j;p
@D le]a[I6[czoj ,qo s^n glAo;q’,qo gryjo.-hl6fD ສະຫງສ.ວວນ.ລິສຂະສິດ
C
AB gxaoglAozjkodk’ gryoj ,adcmofh;p d. A
OC gxao ]aflt\u gryoj ,adcmofh;p r s^n R O
B
d
];’Iv[0v’czjo,qo = 2πr s^n πd
8q;1jk’D 9qj’-vdsk];’Iv[0v’czjo,qomuj,uG
dD ]aflt\ugmqjk 8,7 cm;
0D glAozkj odk’gmqkj 104 cm;
[qfcdhG XgIqkgvqk7kj xt,ko0v’ π = 3,14 ?
d Doe.-hl6f 2πr = 2 x 3,14 x 8,7 cm = 54,636 cm;
π0D oe.-hl6f d = 3,14 x 104 cm = 326,56 cm
122
ສະຫງສ.ວວນ.ລິສຂະສິດ#D [qfg/ydsaf
!D oadIPo shv’,!} d 9eo;o $! 7qo]Poc4;dP,vvdde]a’dkpD I6h;jklv’7qo.f
1nosjk’dao 0,8 m. 4k,;kj w]ptsjk’c8zj 6hmu|bj’wxskz6hl5fmhkp,ugmqjk.f L
@D 9eo;o4h;ome,t-kfXoa[ma’g]d W ? muj,u ! 8q;g]d,u9ad9eo;o L @ 8q;g]d,u9ad
9eo;oL # 8q;g]dF $ 8q;g]d ,u9ad9eo;oL
#D gryjo.-h8q;g]d WF !F @F #F $F &F *F (F )F _ c8]j t8q;9adgmnvj grnvj 0Po9eo;o G
dD c8j ! Ivf __ L
0D c8j !WW sk !__ L c8j @WW sk @__ L
$D ,Ng-QkoU,usvp8q;|bj’8qdlhk’-b’j ,u7;k,g]yd
!W c,afF 8vodk’g;ao,ao0Bo $ c,afF
c8j;jk8vodk’7noraf]q’7no @ c,afD
4k,;kj fqoxko.f,ao9bj’9t0Bos;yfxkdlhk’L
&D xB, @! sq; 4nd;k’g8a’daow;hD ];’l6’0v’dv’xB,oU,u 89 cm D Ih6;jkxB,[k’-toyf
,u7;k,|k 5 cm, 9eo;o|b’j ,u7;k,|k 3 cm. 4k,;kj xB,c8]j t-toyf,u9adsq;
Xxt8y[af8k,;ymu]5j,oU?L
dD lq,,5f;jk .o @! sq;oAo,uxB,c8-j toyfmuj,u7;k,|k 3 cm. dv’xB,9tl6’GD D D D D D
c]t ,ao9ts^5f];’l6’gfu,G D D D D D D D D
0D 7;k,|k0v’xB,ma’lv’-toyf9ts^5fdaoG D D D D D
7D 4hkgvqk7;k,s^5f]noj daomuwj fh.o0=h d ,ksko.sh7;k,s^5f]njomujwfh.o0=h 0 9twfhG
D D D D D D g-yj’c,jo9eo;oxB,-toyfmuj|k 5 cm D
’D lts^5[G D D D D
123
*D wdjxts^kf8q;|bj’;k’w0j !_ |j;p8k,c4;-njF lv’|j;p.fskj ’dao # c,afD
4k,;kj w]ptskj ’c8[j vj o,aovvdw0j|j;pmevyfwxsk|;j pl5fmhkp,ugmqkj .f L
(D 9qj’xP[mP[];’pk;0v’lv’glAosad]5,j oU3fp[+.sh.h-hv5xtdvoD c]h;d;f7no
fh;pdko;afcmdD
)D .shI6[9t85]af WORK
mu,j u];’Iv[gmqkj 32 m. W O
R
gryoj c[j’I6[fa’j djk;vvd gxao ສະຫງສ.ວວນ.ລິສຂະສິດ
# I6[lucj 9lkd gmqkj dao
XI6[g[Nv’0;k?D 9qj’-vdsk
];’Iv[0v’I6[lulj kd c8j
]tvaoD K
_D 9q’j 8n,j 8k8t]k’]5,j oUG
];’d;hk’0v’I6[lujc9lkd ];’pk;0v’I6[lucj 9lkd ];’Iv[0v’
I6[lucj 9lkd
15,2 cm 28,4 cm
24,5 cm
8,06 cm 32,8 cm
16,9 cm 25,5 cm
8,07 cm 10,7 cm 27,4 cm
124
!WD 9qj’-vdsk];’Iv[0v’I6[]5j,oU8k, a c]t b :
1,3 cm
b
a
!!D I6[;q’,qo|bj’,uglAozkj odk’gmqjk 12 cmD9q’j -vdsk];’Iv[0v’I6[9t85]af D
ສະຫງສ.ວວນ.ລິສຂະສິດ
!@D I6[lk,c9 TEA ,u];’Iv[ 12 cm D9qj’-vdsk];’Iv[0v’I6[lucj 9lkd TEAK
I6h;kj AT = 5 cm. T K
!#D 9qj’lhk’I6[ ( c9D E A
dD ,uglAogoaj’9v,ma’\qfgmqkj .fL
0D ,uI6[lk,c9ma’\qf9adI6[L
7D 9q’j xP[mP[9eo;oI6[lk,c9 da[9eo;o0hk’0v’I6[s^kpc9D
!$D dD 9qj’lhk’I6[ # c9mPj ’ ABC, Ih6;kj G AB = BC = 4,5 cm.
0D 9qj’lhk’I6[ # c9ltg\u ABC muj,u0hk’gmqjk 4,8 cm.
7D 9q’j lhk’I6[lucj 90hk’0t|ko ABCD 3fp;jk AB = 6,5 cm c]t BC = 4 cm.
’D 9qj’lhk’I6[lucj 90hk’0t|ko MNPQ 3fp;jk NP = 5,8 cm c]t glAogoa’j 9v,
NQ = 4 cm.
125
ສະຫງສ.ວວນ.ລິສຂະສິດ!&D 8k,czomuj]5,j oU w]ptmk’c8sj ^;’rt[k’wxsk-eg|nvc,oj 1,6 cm. c8oj t7vo
s^;’;P’9aowxsk -eg|nvc,oj 2,6 cm. 9qj’oe.-hv5xtdvo mujg\ktlq,grnjv\kp
mu8j A’0v’-eg|nv.ljczomuj]5j,oUD
!*D l;o8vo|bj’gxaoI6[ $ c9lkd ,u];’pk;cmdwfh 36 m. ];’d;hk’cmdwfh
25 m gryjoxads^adIQ;vhv,l;o sjk’dao]ts;kj ’lv’s^ad 1,5 m. 4k,;kj gryjo8hv’
dkos^adIQ;ma’\qf9adsa^dL
!(D dD 9qj’c8h,;q’,qomu,j u];’Iv[gmqjk 12 cm .shgvqk π = 3
0D 9q’j c8h,I6[lujc9lkdmuj,u];’Iv[gmqkj 12 cm.
7D 9q’j c8h,I6[9t85]afmu,j u];’Iv[gmqkj 12 cm.
!)D 9q’j ;k’g,af A, B c]t C .lgj lAo-nj8k,]efa[ 3fp;jk AB = 42 cm c]t BC = 58 cm.
.shg,af I gxaog,afg7yj’dk’0v’ mjvo-n j AB c]t J gxaog,afg7yj’dk’0v’ mjvo-n j BC.
9q’j 7yfw]j ];’pk; IJ.
126
!_D svp $ 38wx8k,mk’muxj 6fh;p8kdk3imuj,u0t|kfgmqkj daoD glAomk’gfuoc8j]t
38wfhltcf’fa’j I6[]5,j oUG G
38mu ! wxwfh 36 cm
38mu @ wxwfh 48 cm
38mu # wxwfh gmjkq .dL
38mu $ wxwfhgmqjk.f L
X4vf9kd[Aoc0’j 0ao7toyflkf 9y’39h @WW#F Kangaroo 2003)
@WD 9qj’-vdskw]ptmk’c8j A sk B -b’j ltcf’fh;pI6[]5,j oUX\kpgsfG .oI6[oU[+
c,jo];’pk;8q;9y’?G
100cm
A
1 cm
ສະຫງສ.ວວນ.ລິສຂະສິດ
100cm
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
B
9kd[qfg]d c0j’0ao7toyflkf 9y’39h @WW#
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127
@#D 9qj’;k’g,af O(0), A(4) c]t B(7) 16jgmy’cdo9eo;oD c]h;0ufglAo-nj d 8A’lkdda[
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128
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129
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0D .-hg9hp0k; 0ufglAo-nj d c]t \kpg,af A 1j6ovdglAo-nj d. 9kdoAo .-h[aomafF [ao
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131
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132
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ID ;k’g,af B .ljglAodqj’ L D
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133
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134
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d;f7nofh;p dko.-hg9ApdkogdD
135
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136
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{ vjko7kj 0v’,5,16j[aomafcmd,5, g-yj’g8a’da[0hk’mulj v’0v’,5,D .od=]touoU gIqkwfh
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141
#D [qfg/ydsaf A
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@D .oI6[0v’[qfg/ydsaf 0=h !F 9q’j [vd-n0j v’,5,mu,j u9v, I ,k.shwfh !W ,5,D
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0D 9qj’[vd-n0j v’,5,lkdF -n0j v’,5,rP’D
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vaofP;daoD gryjogvUo ,5, xnOz c]t ynOt ;jk ,5,0hk,9v,D 9q’j xP[mP[7kj 0v’
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142
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143
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144
!(D 9q’j c8h,lk,,5, xnAy, znBt, unCv 3fp;jkG xnAy = 50D , zmBt = 90D , unCv = 144D D
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!_D 9qj’c8h,I6[lk,c9 ABC 3fp;kj
AB= 8 cm, CnAB = 48°, CnBA = 84°
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dD 0ufglAo-nj ( xy) , \kpg,af B
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@@D A
dD 9qj’[vdxtgrf0v’I6[lk,c9
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145
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dD 9q’j c8h,I6[lk,c9 ABC 3fp;jkG AB= 7 cm, BC= 6 cm, CA= 5 cm
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@$D .oc8j]tou8+wxoUF 9q’j 7yfw]j7jk;afcmd0v’,5, xnOy D
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@*D 9q’j lhk’I6[lk,c9lkd ABC lkd16j9v, B 3fp;kj AB = 5 cm , BnAC = 35D.
146