Mensuration

1. The perimeters of two equilateral

triangles are in the ratio of 4:1. What 4. The sides of a triangle are in the
is the ratio of their areas? ratio 3:4:5. If its perimeter is 36 cm,
(a) 2:1 area of the triangle is
(b) 4:1 (a) 57 sq cm
(c) 16:1 (b) 54 sq cm
(d) 8:1 (c) 56 sq cm
(d) None of the above

2. What is the area of an equilateral

triangle of side 16 cm? 5. The Perimeter of a rectangular field
(a) 64 √3 cm2 is 480 meters and the ratio between
(b) 128√3 cm2 the length and breadth is 5:3. The
(c) 96√3 cm2 area of the field is
(d) 32√3 cm2 (a) 7200 m2
(b) 15000 m2
(c) 13500 m2
(d) None of the above

3. A wire is bent to form a rectangle of

length 16 cm and breadth 6 cm. If it 6. A room is 13m long, 9m broad and
is bent to form a circle, what is the 5m height. Find the cost of painting
circle’s area? the walls of the room at Rs. 45 per
(a) 150 cm2 sq metres, it being given that the
(b) 128 cm2 doors and windows occupy 60 sq
(c) 154 cm2 metres.
(d) 308 cm2 (a) Rs.6400
(b) Rs.7000
(c) Rs.7200
(d) Rs.5400

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 Mensuration
(b) 192 sqm
(c) 196 sqm
7. How many metres of a carpet, 75 (d) 200 sqm
cm wide, will be required to cover
the floor of a room which is 20 10. If the length of a rectangle is
metres long and 12 metres broad? increased by 30% and breadth is
(a) 340m increased by 20%. What is the
(b) 360m increased percentage in area?
(c) 320m (a) 64%
(d) 400m (b) 56%
(c) 44%
(d) 60%

8. A room 8 metres long, 6 metres

broad and 3 metres high has two
windows 1½m x 1m and a door 2m 11. If the length of a rectangle is
x 1½ m. Find the cost of papering increased by 30% and breadth is
the walls with paper 50cm wide at decreased by 20%. What is the
Rs. 25 per metre. percentage change in area?
(a) Rs. 4000 (a) 8%
(b) Rs. 4200 (b) 6%
(c) Rs. 3900 (c) 4%
(d) Rs. 4500 (d) 10%

9. A hall, whose length is 16 metres 12. The diameter of a coin is 2cm. If

and breadth twice its height, takes four of these coins be placed on a
168 metres of paper, 2 metres wide, table so that the rim of each touches
for its four walls. Find the area of that of the other two. Find the area
the floor? of the unoccupied space between
(a) 212 sqm them.
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 Mensuration
(a) (8-⊼) (c) 10√2%
(b) (6-⊼) (d) None
(c) (4-⊼)
(d) (2-⊼)

13. If the sides of a square are

increased by 10%, then its area is
increased by what percent? 16. If the six sides of a regular hexagon
(a) 10% is increased by 30%. What is the
(b) 20% increase in its area?
(c) 21% (a) 30%
(d) 25% (b) 60%
(c) 69%
(d) None of the above

14. If the sides of a rectangle are

increased each by 10% what is the
percent increase in its diagonals? 17. Two poles, 15m and 30m high,
(a) 10% stand upright in a playground. If
(b) 20% their feet be 36m apart, find the
(c) 30% distance between their tops?
(d) 40% (a) 29 cm
(b) 30 cm
(c) 39 cm
(d) None

15. If the sides of a square is increased

by 10√2%. What is the percent
increase in its perimeter? 18. The area of a square and
(a) 42√2% rectangular field is 900m2 each. If
(b) 25√2% the perimeter of the rectangular field
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 Mensuration
is 2m more than that of the square (b) 412 m2
field, calculate the length and (c) 616 m2
breadth of the rectangular field? (d) None
(a) 24m, 10m
(b) 30m, 25m
(c) 36m, 25m
(d) 36m, 24m
22. The area of a parallelogram is 240
19. A rectangular park 18m x 12m is cm2and its height is 12xcm. The
surrounded by a path 4m wide from base of the parallelogram is-
outside. Find the area of the path (a) 24 cm
(a) 304 m2 (b) 20cm
(b) 308 m2 (c) 28cm
(c) 310 m2 (d) None
(d) 312 m2

23. The wheel of a scooter has diameter

20. Find the area of largest circle 70cm. How many revolutions per
inscribed on a square of side 28cm. minute must the wheel make so that
(a) 616 cm2 the speed of the scooter is kept
(b) 312 cm2 66km per hour?
(c) 216 cm2 (a) 400
(d) None (b) 600
(c) 500
(d) 800

21. Find the area of largest circle

circumscribed in a square of side 14 24. A circular road runs round a circular
√2m? ground. If the difference between
(a) 512 m2 the circumferences of the outer
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 Mensuration
circle and the inner circle is 66 breadth. Find the cost of gravelling
metres, then find the width of the them at Rs.20 per sqm?
road? (a) Rs.25000
(a) 21m (b) Rs.27000
(b) 10.5m (c) Rs.24000
(c) 7 m (d) Rs.26000
(d) None

28. The ratio of the length of the parallel

25. If a regular hexagon is inscribed in a sides of a trapezium is 3:2. The
circle of radius r, then find the shortest distance between them is
perimeter of regular hexagon? 15cm. If the area of the trapezium
(a) 7r is 450 sqcm, find the sum of the
(b) 5r lengths of the parallel sides?
(c) 6r (a) 40cm
(d) 8r (b) 50cm
(c) 75cm
(d) None

26. The perimeter of a rhombus is 29. The length and the breadth of a
40cm. If the length of one of its rectangular plot are in the ratio of
diagonal be 12cm, then find the 5:3. The owner spends Rs.3000 for
length of other diagonal? surrounding it from all the sides at
(a) 14cm the rate of Rs.7.5 per metre. What
(b) 15cm is the difference between length and
(c) 16cm breadth of the plot?
(d) 12cm (a) 40m
(b) 50m
(c) 75m
(d) None

27. A rectangular lawn 80m x 60m has

two roads each 10m wide running in
the middle of it, one parallel to the 30. Find the length of the rope by which
length and the other parallel to the a cow must be tethered in order that
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 Mensuration
it may be able to graze an area of (b) 5m
154 SQm. (c) 7m
(a) 10m (d) 15m