Sheet MENSURATION – 2D

03
– 2D
1. n a rectangle _____. 5. Area of a rectangle is 240 cm². The sum of the
length of a diagonal and length of rectangle is 5
times of its breadth. Find the length of the rect-
(a) Consecutive angles are congruent as well as
angle.
supplementary/
²

(b) Diagonals are perpendicular to each other

(a) 10 cm (b) 4.2 cm

(c) Diagonals bisect opposite angles
(c) 24 cm (d) 8.4 cm
6. Area of a rectangle is 2250 cm². If the length of a
(d) Diagonals are not equal rectangle is increased by 5 cm then area of the
rectangle is increased by 225 cm² then find the
2. Area of rectangle is 120 cm². Length of the rect- breadth of the rectangle.
angle is increased in the ratio of 5 : 6 and its ²
breadth is reduced in the ratio of 3 : 2. The find ²
new the rectangle.
² (a) 45 cm (b) 4.2 cm
(c) 2.4 cm (d) 8.4 cm

3
(a) 96 cm² (b) 216 cm² 7. The length of a rectangle is times of its breadth.
(c) 144 cm² (d) 1500 cm² 2
3. Ratio of the length to the breadth of rectangle is 3 If the length of the rectangle is increased by 5 cm
: 2. Each side of rectangle is increased by 1 cm and the breadth is reduced by 5 cm then its area
from the both sides. The new ratio of the length to is decreased by 115 cm². Find its original length
the breadth becomes 10 : 7. Find the initial area and breadth ?
of the rectangle ?
3
2

(a) 96 cm² (b) 216 cm²

(a) 54 cm, 36 cm (b) 18 cm, 12 cm
(c) 144 cm² (d) 1500 cm²
(c) 27 cm, 18 cm (d) 6 cm, 3 cm
4. Ratio of the length and the breadth of a rectangle
is 3 : 2. Each side of the rectangle is reduced by 5 8. The area of a rectangle is 720 cm². If the length is
cm in both sides then the new ratio becomes 5 : 3. increased by 4 cm and the breadth is decreased
Find the new area of the rectangle. by 1 cm then its area is increased by 40 cm². Find
the difference between 4 times of its breadth and
its length?
²

(a) 96 cm² (b) 216 cm² ²

(c) 144 cm² (d) 1500 cm²

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 (a) 8 cm (b) 16 cm (a) 4 : 3 (b) 8 : 9 (c) 3 : 4 (d) 9 :
(c) 4 cm (d) 48 cm 8
9. Diagonal of a rectangle is 25 cm. and its perimeter 15. ABCD is a rectangle. L, M, N and O are the mid
is 70 cm. Find the area of the rectangle. points of side AB, BC, CD and AD respectively,
then find the area of quadrilateral LMNO?
ABCD L, M, N O AB,
BC, CD AD LMNO
(a) 300 cm² (b) 1080 cm²
(c) 60 cm² (d) 2000 cm²
10. A person cross a rectangular field diagonally at 1
the speed of 52m/min in 15 sec. Other person B (a) (Area of ABCD)
3
cross the field along its side at the speed of 68m/
min at the same time. Find the area of the field.
1
(b) (Area of ABCD)
4

1
(c) (Area of ABCD)
2
(a) 300 m² (b) 1080 m²
(c) 60 m² (d) 2000 m² 1
(d) (Area of ABCD)
11. The ratio of the length to the breadth of a rectangu- 3
lar field is 5 : 4. A person completes 3 revolution of
around the field at the speed 1.8 km/hr in 18 mins.
Find the area of the field ?
A L B

O M
(a) 300 m² (b) 1080 m²
(c) 60 m² (d) 2000 m²
12. The ratio of the diagonal and the breadth of a rect-
angle is 17 : 8. If the length of the rectangle is 45 D N C
cm. Find the area of the rectangle ?
16. PQRS is a rectangle. A, B, C and D are the mid
points of sides PQ, QR, RS and PS respectively. If
(a) 300 cm² (b) 1080 cm2 area of PQR is 48 cm2 then what is the area (in
(c) 60 cm² (d) 2000 cm² cm ) of
2
BCD?
13. Length of the diagonal of a rectangle is 65 cm and PQRS A B C D PQ,
its perimeter is 170 cm. Find the area ?
QR, RS PS PQR
² BCD ²
(a) 24 (b) 6 (c) 16 (d) 12
(a) 1500 cm² (b) 1200 cm²
(c) 1800 cm² (d) 1000 cm²
14. Perimeter of a rectangle and a square is equal.
The ratio of the two sides of the rectangle is 1 : 2.
Find the ratio of the area of rectangle and area of
the square.

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 S C R (a) 3 2 (b) 5 2

(c) 24 (d) 41

D B A B

Q
P A Q
17. In the given figure area of triangle AOD, COD
and AOB is respectively 8 cm², 12 cm² and 16 D C
cm². Find the area of BOC
20. If O is a point lying outside the rectangle ABCD
AOD, COD AOB and OA = 5, OB = 6, OC = 9. Then find the length
² ² BOC of OD./ ABCD O
OA = 5, OB = 6, OC = 9 OD
(a) 20 (b) 6 (c) 16 (d) 12
(a) 72 (b) 74
D C
(c) 76 (d) 78
21. PQRS is a rectangle in which PQ = 24, QR = 16, T
is a point on RS. What is the area of PTQ?
O
PQRS PQ = 24, QR = 16 RS
T PTQ
(a) 192 cm² (b) 168 cm²
A B
18. O is a point situated inside a rectangle, ABCD. If (c) 148 cm² (d) 162 cm²
sides OA, OC and OD are 6 cm, 8 cm and 6 cm S T R
respectively, then find the value of OB
ABCD O OA, OC
OD OB
(a) 4cm (b) 6cm (c) 8cm (d) 10cm
A B
P Q
22. PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ABC
is a triangle whose vertices lie on the sides of PQRA
O such that BQ = 2 cm and QC = 16 cm. Then the
length of the line joining the mid points of the sides
AB and BC is.
PQRA AP = 22 PQ = 8 ABC
D C PQRA BQ
19. Q is a point in the interior of a rectangle ABCD, if
=2 QC = 16 AB BC
QA = 3 cm, QB = 4 cm and QC = 5 cm then the
length of QD ( in cm) is
ABCD Q QA = 3 cm, QB = 4 (a) 4 2 cm (b) 5 cm
cm QC = 5 cm QD (cm )
(c) 6 cm (d) 10 cm

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 P A PMRN PQRS

(a) 34 cm2 (b) 51 cm2 (c) 68 cm2 (d) 85 cm2

Q C R
23. In the given figure, ABCD is a rectangle and P is a
point on DC such that BC = 24 cm, DP=10 cm and
CD = 15 cm. If AP produced intersects BC pro-
duced at Q, then the length of AQ.
ABCD DC P 26. In the figure given below ABCD is a rectangle. The
BC = 24 DP = 10 CD = 15 area of the isosceles right triangle ABE = 7 cm²,
EC = 3BE cm. The area of ABCD (in cm²) is?
AP BC Q
ABCD ABE
AQ
7 cm2 CE = 3 BE ABCD
(a) 24 cm (b) 26 cm
(c) 39 cm (d) 35 cm
A D (a) 28 (b) 49 (c) 56 (d) N.O.T

Q
B C
24. ABCD is a rectangle where the ratio of the length
of AB and BC is 3 : 2. If P is the mid- point of AB,
then the value of sin  CPB is
ABCD AB BC 27. In a given figure ABCD is a rectangle. The area of
P AB sin  CPB isosceles right triangle BCE is 14 cm. and DE = 3
EC then area of ABCD is -
ABCD BCE
3 2 3 4 DE = 3, EC ABCD
(a) (b) (c) (d)
5 5 4 5
(a) 56 sq.cm (b) 84 sq.cm
D C
(c) 112 sq.cm (d) 3 28 sq.cm

A P B
25. In the given figure, PM is one-third of PQ and PN
is one-third of PS. If the area of PMRN is 17 cm2,
then what is the area (in cm2) of PQRS ?
28. ABCD is a rectangle given in figure in which AD =
PM, PQ PN, PS 4 unit and AE = EB. EF is perpendicular to DB

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 and half of DF. The area of DEF is 5 unit then
(a) 2 : 1 (b) 3 –1:1
what is the area of ABCD?
ABCD AD = 4 (c) 3 +1 : 1 (d) 2: 3
AE = EB. EF, DB DF
1. Length and breadth of rectangular field is 38 metre
DEF ABCD and 32 metre respectively. A road of uniform width
is built inside the rectangular field. If the area of
(a) 20 sq. unit (b) 24 sq. unit road is 600m2. then find of the breadth of the road.

(c) 28 sq. unit (d) 18 3 sq. unit

(a) 5 (b) 10 (c) 2.5 (d) 7.5

2. Length and breadth of a rectangular field are 160
metre and 45 metre respectively. A road of uni-
form width is built inside the rectangular field. If
the area of the road is 1000 m2. then find the
breadth of the road ?

29. ABCD is a rectangle. P is a point on the side AB as

shown in the given figure. If DP = 13, CP = 10 and
(a) 2.5 metre (b) 5 metre
BP = 6, then what is the value of AP
(c) 10 metre (d) 8 metre
ABCD P AB
1. Length and breadth of a rectangular field is 45
DP = 13, CP = 10 BP = metre and 25 metre. Respectively 2.5 m wide road
6 AP is built outside along the field.

(a) 105 (b) 133 (c) 12 (d) 10

(i) Find the total perimeter of the road

(ii) Find the area of the road/

(a) 375, 300 (b) 300, 375
(c) 325, 350 (d) 350, 325
2. Length and breadth of rectangular field are 40
metre and 30 metre respectively. A road of uni-
form width is built outside the rectangular field.
If area of the road is 375m2. Find the breadth of
the road.

30. If L, b, p be the length, breadth and perimeter of a

rectangle and b, L, p are in G.P. (in order) then (a) 5 (b) 2.5 (c) 10 (d) 7.5
1. Length and breadth of a rectangular field are 80
L metre and 60 metre. It has 2 roads, each is 10 m
=?
b wide running in the middle of it, one is parallel to
length and other is parallel its breadth. Find the
L, b, p b,
area of the road?
L
L, p =?
b

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 3. If the width of the path around a square field is
4.5 m and the area of the path is 252 m², then the
(a) 1300 m2 (b) 1100 m2 length of the side of the field is:
(c) 1500 m2 (d) 1400 m2
2. Length and breadth of rectangular field are re-
spectively 90 metre and 70 metre. It has 2 roads
of uniform width running in the middle of it, one
(a) 9.5 m (b) 9 m (c) 8 m (d) 8.5 m
is parallel to the length and other is parallel to the
breadth. If the area of the road is 624m2 then find
the width of the road ?

(a) 3 m (b) 8 m (c) 4 m (d) 5 m

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