Class

04 GEOMETRY

1. In the given figure, find the area of  ABC ?

 ABC
(a) 10 2 (b) 15 2
(c) 20 2 (d) 25 2

4. If three sides of a triangle are 8 cm, 17 cm and x cm,

for what value of x, area of triangle is maximum?
x x

2. In the given figure, find the area of  ABC ? (a) 15 cm (b) 17 cm

 ABC (c) 18.79 cm (d) 23.16 cm
5. If three sides of a triangle are 6 cm, 10 cm and y cm,
(a) 5 (b) 10 (c) 15 (d) 20
for what value of y, area of triangle is maximum?
y y

(a) 12.02 cm (b) 8 cm

(c) 11.66 cm (d) 8.99 cm
6. For what value of x, area of triangle is maximum,
If three sides of a triangle are x cm, 5 cm and 7
cm?/ x
x
(a) 5.12 cm (b) 7.69 cm
(c) 8.79 cm (d) 8.60 cm
3. In the given figure, find the area of  ABC ? 1. In triangle ABC,  A = 60°, AB = 3 cm and AC = 4
 ABC cm. Find the value of AD. If AD is an angle bisec-
tor./ ABC  A = 60° AB = 3 AC = 4
9 3 10 3 AD AD
(a) (b)
2 2
12 3 12 5
(a) (b)
11 3 12 3 7 7
(c) (d)
2 2 12 11 12 7
(c) (d)
7 7

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2. In a  PQR,  PQR = 90°, S is a point on side PR
such that  PQS = 45°. If PQ = 16 cm and QR = 15
cm, then find the length of QS ?/ PQR  PQR
= 90° PR S  PQS
= 45° PQ = 16 QR = 15 QS

240 2 120 10
(a) (b)
31 23 + 8 3
240 2 480 2
(c) (d)
62 31
3. In the given figure AD : BD = 1 : 2, AE : EC = 3 : 4,
3. In a  ABC, AB = 8 cm, AC = 12 cm, AD is the
Areaof triangle ADE
angle bisector of  BAC. Given that BAC = 60°.
What is the length of AD./ ABC AB = 8 Area of triangle ABC = ?
cm, AC = 12 cm, AD AD  BAC (a) 1 : 9 (b) 1 : 8 (c) 1 : 6 (d) 1 : 7
BAC = 60° AD

24 3 24 3
(a) (b)
5 7
24 3 24 3
(c) (d)
11 13

1. Area of  ADE : Area of  ABC = ?

 ADE  ABC =? 4. In the given figure, Triangle PQR. S and T are two
(a) 1 : 9 (b) 1 : 8 (c) 1 : 6 (d) 1 : 7 points on side PQ and PR respectively such that PS
: SQ = 3 : 4 and PT : TR = 6 : 5 if Area of STRQ =
177 cm2 Then find the area of  PQR?
PQR S T PQ PR
PS : SQ = 3 : 4 PT : TR = 6 : 5
STRQ 2
 PQR

s
(a) 198 (b) 231 (c) 190 (d) 264

2. Area of triangle ADE : Area of BCED = ?

 ADE BCED =?
(a) 1 : 9 (b) 1 : 8 (c) 1 : 6 (d) 1 : 7

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5. Find BD in the given figure: CD?
BD ABC BC = 5 AC
48 36 = 12 AB D
(a) b)  BCD = 30° CD
3 3+4 3 3+4
47 45 60 17
(c) (d) (a) cm (b) cm
3 3+4 3 3+4 13 2

120 120
(c) cm (d) cm
5 + 12 3 5 – 12 3

6. In the given figure, AD = 3, DE = 4, AB = 12, BF =

M 8. In the given figure, PQR is a triangle and quadrilat-
2, FG = 6, BC = 10, then the value of is: (As- eral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm,
N
sume : M is the area of the quadrilateral FGDE and CR = 3 cm, BR = 4 cm, PB = 6 cm, PA = 5 cm and AD
N is the area of the triangle ABC.)/ = 3. What is the area (in cm²) of the quadrilateral
ABCD?
AD = 3, DE = 4, AB = 12, BF = 2, FG =
PQR ABCD
M
6, BC = 10 M QD = 2 QC = 5 CR = 3
N
BR = 4 PB = 6 PA = 5 AD = 3
FGDE N ABC
ABCD 2

31 1 25 1
(a) (b) (c) (d)
60 2 49 3 23 21 15 21
(a) (b)
4 4

17 21 23 21
(c) (d)
5 5

7. Let ABC be a right angled triangle with BC = 5 cm

and AC = 12 cm. Let D be a point on the hypot-
enuse AB such that  BCD = 30°. What is length of

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 A

B C

11. In the given figure if PT = 4, RT = 8, RS = 6, QR = 4

9. In the given figure, AG = GF = 4 cm, FE = 2 cm,
then find the ratio of, area of  PQR and  STR.
ED = 17 cm, CD = 6 cm, BC = 10 cm and AB = 5
PT = 4, RT = 8, RS = 6, QR = 4
cm find the area of BCFG.
AG = GF = 4 cm, FE = 2 cm, ED =  PQR  STR
17 cm, CD = 6 cm, BC = 10 cm AB = 5 cm (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 2 : 3
BCFG P
(a) 48 cm² (b) 84 cm²
(c) 36 cm² (d) 40 cm²

Q R S
12. In the given figure AD = x, DB = b, DE = y, DC = a
10. In the given figure AD = 3, DB = 2, DE = 4, if area of then find the value of x × y. If area of  ADE &
 ADE and  BDC are equal then find the length  BDC are equal./ AD = x, DB = b, DE
of EC./ AD = 3, DB = 2, DE = 4 = y, DC = a x×y  ADE
 ADE  BDC EC  BDC
(a) a² b (b) b² a
(a) 1 (b) 2 (c) 3 (d) 4 (c) ab (d) N.O.T

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 A
(a) 4 2 (b) 8 2 (c) 5 2 (d) 3 2

b a E

B C
13. In the given figure if ST = 8, TU = 9, SU = 12 QU =
ar. of ΔPQU
24, SR = 32, PT = 27, then find
ar. of ΔPTR = π
3. In triangle ABC, if b = 3, c = 4 and B = , then
3
?/ ST = 8, TU = 9, SU = 12 QU = 24, SR
number of such triangles is:
ar. of ΔPQU π
= 32, PT = 27 ABC b = 3, c = 4 B =
ar. of ΔPTR 3
2 4 2 4
(a) (b) (c) (d)
3 9 9 3 (a) 1 (b) 2
P
(c) 0 (d) infinite

U
S

Q R

1. In the triangle

ABC,  A = 30°,  B = 45° AC = 3 2 , BC = ?

(a) 1 (b) 2 (c) 3 (d) 4

2. Find AC = ?, If  A = 60°,  B = 45°, BC = 4 3

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