Chapter 2t
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2. ntjugt
2.1! hvh
hml
l 2 + b 2 !nzGgt<
2.1.2! -j{gvl;: hvh
2.1.3
hml< 2.2
ogiMg
1 b × h sKv!nzGgt<. 2
hml
32
2.1.4! osr
hml< 2.4
b 2 + h 2 !nzGgt<
2.1.5 slhg
hml
2.1.6! -Vslhg
hvh
)
(
Sx<xtU = 2 a + a 2 − h 2 !nzGgt< 2.1.7! nslhg
s ( s − a)(s − b)(s − c) s/n a+b+c -r
hvh
2.1.8
hml< 2.7
siqugl<; hvh
hml< 2.8
1 (a + b) × h sKv!nzGgt< 2
2.1.9! fix
1 d × (h1 + h2). 2 sKv!nzGgt<
hml
2.1.10!sib<sKvl<; 1 hvh
2
hml< 2.10
= 4a nzGgt<
33
2.1.11!um<ml<: um<mk
hml
Gxqh
5 2 − 32
= 16 = 4!lQ/ siqugl
35
hml
wMk
2
weg
2
= 20 os/lQ! nz
2
-r
3 3 × a2 = × 44 2 4 4
= 484
3 os/lQ2
∴ um<ml
hml< 2.21
uqgqkl
! hbqx<sq 2.1 1.
gQp
2.
3.
4.! 5. 6. 7.
8.
2.2
ABCD we<x!fix
nf
%m<M dVur
yV! fix
37
WkiuokiV!hg
hml< 2.24
hml< 2.26
hml< 2.25
hml
hml< 2.27 hml< 2.28
hml< 2.31
hml< 2.30
hml< 2.33 hml< 2.32 38
hml< 2.34 hml< 2.35 ye<xqe
siqugl< siqugl
hg
DC Bl
glk; 2.36 1 ×a×h ! ∆ABC bqe
39
hz
nXOgi{k
CF sf
3 2 a NGl
3 2 3 3 2 a = a sKv nzGgt
! wMk
hml< 2.38
1 1 ( a + b ) × h = (10 + 16 ) × 9 = 117 os/l P 2 . 2 2
BCD yV!Lg
∴!%m<M!dVul< ABCDE!e
hml
kQIU: A! bqzqVf
siqugl< PRCB! e
2 1 2
(10 + 8) × 7 = 63 lQ2
hml< 2.40
siqugl
-j{! hg
Lg
2
× AQ × FQ = 1 × 7 × 8 = 28 lQ2
1 2 1 2
× DS × ES =
2 1 2
×(AD − AS) × 9
= 1 (17 − 15) × 9 = 1 × 2 × 9 = 9 lQ2. 2
Lg
1 2
× RD × CR
2
=1 2
× (AD − AR) × 8
= 4 × (17 − 12)= 4 × 5 = 20 lQ2. Lg
2
∴!fqzk
41
wMk
weh
hml< 2. 41
kQIU;! osu
2
slhg
3 4
7
a = 3 × 14 × 14 = 49 3 os/lQ2. 2
4
∴ ljebqe
weh
glk; 2.42 kQIU; osu
7
7
7
4 giz
42
wMk
hml< 2.43 kQIU;! -h
2 e
× 22 × 14 × 14 = 22 × 14 = 308 os.lQ2 7
∴ ogiMg
hml
43
wMk
hml< 2.45 kQIU;! ogiMg
4
7
∴!Okjubie!hvh
! ! ! ! glk; 2.46 ! ! kQIU;! dt
2 × 22
weOu!dt
2
7
7
44
yV!osu
kQIU;!sKvk
4 4 3 × 22 × 4.9 × 4.9 + 1 × 22 × 4 7 2 7 33 × 0.7 × 4.9 + 11 × 0.1 × 0.7 2
0.7 × 0.7
= 56. 595 + 0.77 = 57.365lQ2. hml< 2.47 ! wMk
weg
hml< 2.48
kQIU;!fqpzqmh
2 1 2
2
×
22 7
× 14 × 14 − 1 × 22 × 7 × 7 = 11 × 2 × 14 − 11 × 7 = 308 − 77 = 231 os.lQ2. 2
7
! !
45
hbqx<sq 2.2 1.
fqzlth
(ii)
(i)
hml
hml
hml
yV! uqjtbim<M! jlkiel
3.
yV!siqugk
YI!yPr
4.
5.
3
os.lQ2 weqz
hml
! hml
46
6. gQp
(ii)
hml
(iv)
hml
hml
yV!um<mk nke
8.
hml
hml
14 lQ hg
gm<mh
weg
ABCD? 36lQ × 24lQ ntUt
47
uqjmgt; hbqx<sq 2.1 1.
(i) 27 os.lQ2
(ii) 480 os.lQ2
(iii) 27.71 os.lQ2
2.
704 os.lQ2
3. 60os.lQ2
4. 112 lQ? 3696 lQ2
5.
34 os.lQ
6. 4 os.lQ
7. 10 os.lQ
8.
62.22os.lQ hbqx<sq!2.2
1.
(i) 27?200 s/lQ
2.
4?956!s/lQ
5.
140 lQ2
6.
(i) 36.39!s/os.lQ
7.
770 os.lQ2
(ii) 15?100 s/lQ 3. 147.22 os.lQ2 (ii) 25 lQ2
(iii) 7?525 s/lQ 4. 10 os.lQ
(iii) 37.71 os.lQ2
8. 354.37 os.lQ2? 94 os.lQ 9. 42 lQ2
48
(iv) 240.28 os.lQ2 10. 549.71lQ2
2.1! hvh
hml
l 2 + b 2 !nzGgt<
2.1.2! -j{gvl;: hvh
2.1.3
hml< 2.2
ogiMg
1 b × h sKv!nzGgt<. 2
hml
32
2.1.4! osr
hml< 2.4
b 2 + h 2 !nzGgt<
2.1.5 slhg
hml
2.1.6! -Vslhg
hvh
)
(
Sx<xtU = 2 a + a 2 − h 2 !nzGgt< 2.1.7! nslhg
s ( s − a)(s − b)(s − c) s/n a+b+c -r
hvh
2.1.8
hml< 2.7
siqugl<; hvh
hml< 2.8
1 (a + b) × h sKv!nzGgt< 2
2.1.9! fix
1 d × (h1 + h2). 2 sKv!nzGgt<
hml
2.1.10!sib<sKvl<; 1 hvh
2
hml< 2.10
= 4a nzGgt<
33
2.1.11!um<ml<: um<mk
hml
Gxqh
5 2 − 32
= 16 = 4!lQ/ siqugl
35
hml
wMk
2
weg
2
= 20 os/lQ! nz
2
-r
3 3 × a2 = × 44 2 4 4
= 484
3 os/lQ2
∴ um<ml
hml< 2.21
uqgqkl
! hbqx<sq 2.1 1.
gQp
2.
3.
4.! 5. 6. 7.
8.
2.2
ABCD we<x!fix
nf
%m<M dVur
yV! fix
37
WkiuokiV!hg
hml< 2.24
hml< 2.26
hml< 2.25
hml
hml< 2.27 hml< 2.28
hml< 2.31
hml< 2.30
hml< 2.33 hml< 2.32 38
hml< 2.34 hml< 2.35 ye<xqe
siqugl< siqugl
hg
DC Bl
glk; 2.36 1 ×a×h ! ∆ABC bqe
39
hz
nXOgi{k
CF sf
3 2 a NGl
3 2 3 3 2 a = a sKv nzGgt
! wMk
hml< 2.38
1 1 ( a + b ) × h = (10 + 16 ) × 9 = 117 os/l P 2 . 2 2
BCD yV!Lg
∴!%m<M!dVul< ABCDE!e
hml
kQIU: A! bqzqVf
siqugl< PRCB! e
2 1 2
(10 + 8) × 7 = 63 lQ2
hml< 2.40
siqugl
-j{! hg
Lg
2
× AQ × FQ = 1 × 7 × 8 = 28 lQ2
1 2 1 2
× DS × ES =
2 1 2
×(AD − AS) × 9
= 1 (17 − 15) × 9 = 1 × 2 × 9 = 9 lQ2. 2
Lg
1 2
× RD × CR
2
=1 2
× (AD − AR) × 8
= 4 × (17 − 12)= 4 × 5 = 20 lQ2. Lg
2
∴!fqzk
41
wMk
weh
hml< 2. 41
kQIU;! osu
2
slhg
3 4
7
a = 3 × 14 × 14 = 49 3 os/lQ2. 2
4
∴ ljebqe
weh
glk; 2.42 kQIU; osu
7
7
7
4 giz
42
wMk
hml< 2.43 kQIU;! -h
2 e
× 22 × 14 × 14 = 22 × 14 = 308 os.lQ2 7
∴ ogiMg
hml
43
wMk
hml< 2.45 kQIU;! ogiMg
4
7
∴!Okjubie!hvh
! ! ! ! glk; 2.46 ! ! kQIU;! dt
2 × 22
weOu!dt
2
7
7
44
yV!osu
kQIU;!sKvk
4 4 3 × 22 × 4.9 × 4.9 + 1 × 22 × 4 7 2 7 33 × 0.7 × 4.9 + 11 × 0.1 × 0.7 2
0.7 × 0.7
= 56. 595 + 0.77 = 57.365lQ2. hml< 2.47 ! wMk
weg
hml< 2.48
kQIU;!fqpzqmh
2 1 2
2
×
22 7
× 14 × 14 − 1 × 22 × 7 × 7 = 11 × 2 × 14 − 11 × 7 = 308 − 77 = 231 os.lQ2. 2
7
! !
45
hbqx<sq 2.2 1.
fqzlth
(ii)
(i)
hml
hml
hml
yV! uqjtbim<M! jlkiel
3.
yV!siqugk
YI!yPr
4.
5.
3
os.lQ2 weqz
hml
! hml
46
6. gQp
(ii)
hml
(iv)
hml
hml
yV!um<mk
8.
hml
hml
14 lQ hg
gm<mh
weg
ABCD? 36lQ × 24lQ ntUt
47
uqjmgt; hbqx<sq 2.1 1.
(i) 27 os.lQ2
(ii) 480 os.lQ2
(iii) 27.71 os.lQ2
2.
704 os.lQ2
3. 60os.lQ2
4. 112 lQ? 3696 lQ2
5.
34 os.lQ
6. 4 os.lQ
7. 10 os.lQ
8.
62.22os.lQ hbqx<sq!2.2
1.
(i) 27?200 s/lQ
2.
4?956!s/lQ
5.
140 lQ2
6.
(i) 36.39!s/os.lQ
7.
770 os.lQ2
(ii) 15?100 s/lQ 3. 147.22 os.lQ2 (ii) 25 lQ2
(iii) 7?525 s/lQ 4. 10 os.lQ
(iii) 37.71 os.lQ2
8. 354.37 os.lQ2? 94 os.lQ 9. 42 lQ2
48
(iv) 240.28 os.lQ2 10. 549.71lQ2
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