AREA QUESTIONS AND ANSWERS

1. The length and breadth of a square are increased by 40$ and 30% respectively. The area of

the resulting rectangle exceeds the area of the square by:

(a) 42%

(b) 62%

(c) 82%

(d) none of these

ANSWER : (c) 82%

2. The length of a rectangular plot is twice its width. If the length of a diagonal is 9 metres, the

perimeter of the rectangle is:

(a) 27 m

(b) 54 m

(c) 84 m

(d) none of these

ANSWER : (b) 54 m

3. The length of a rectangle is increased by 60%. By what per cent would the width have to be

decreased to maintain the same area?

(a) 37 %

(b) 60%

(c) 75%

(d) 120%

ANSWER : (a) 37 %

4. If the ratio of the areas of two squares is 9:1, the ratio of their perimeters is:

(a) 9:1

(b) 3:1

(c) 3:4

(d) 1:3

ANSWER : (b) 3:1

5. If the side of a square is increased by 25% then how much per cent does its area get

increased:

(a) 125

(b) 156.25

(c) 50

(d) 56.25

ANSWER : (d) 56.25

6. A park is 10 metres long and 8 metres broad. What is the length of the longest pole that can

be placed in the park?

(a) 10 metres

(b) 12.8 metres

(c) 13.4 metres

(d) 18 metres

ANSWER : (b)12.8 metres

7. A hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m. the

cost of flooring the verandah at the rate of Rs. 3.50 per sq. metre is:

(a) Rs.500

(b) Rs.600

(c) Rs.700

(d) Rs.800

ANSWER : (c) Rs.700

8. The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. The cost

of putting a fence around it at 75 paise per metre is:

(a) 900

(b) 1800

(c) 360

(d) 810

ANSWER : (a) 900

9. The length of hall is (4/3) times its breadth. If the area of the hall be 300 square metres the

difference between the length and the breadth is:

(a) 15 metres

(b) 4 metres

(c) 3 metres

(d) none of these

ANSWER : (d)none of these

10. The area of a rectangle is three that of a square. Length of the rectangle is 40 cm and the

breadth of the rectangle is (3/2) times that of the side of the square. The side of the square

in cm is:

(a) 15

(b) 20

(c) 30

(d) 60

ANSWER : (b)20

11. Area of a square hectare. The diagonal of the square is:

(a) 250 metres

(b) 100 metres

(c) 100 metres

(d) 50 metres

ANSWER : (b) 100 metres

12. . If the side of a square is doubled then the ratio of the resulting square to that of the given

square is:

(a) 1:2

(b) 2:1

(c) 2:1

(d) 4:1

ANSWER : (d) 4:1

13. The length of a rectangle is doubled while its breadth is halved. What is the percentage

change in area?

(a) 50

(b) 75

(c) no change

(d) no change

ANSWER : (d) no change

14. A rectangle has 15 cm as its length and 150 cm2 as its area. Its area is increased to 1 times

the orginial area by increasing only its length. Its new perimetrer is:

(a) 50 cm

(b) 60 cm

(c) 70 cm

(d) 80 cm

ANSWER : (b) 60

15. One side of a rectangular field is 4 metres and its diagonal is 50 metrs. The area of the field

is:

(a) 12 m2

(b) 15 m2

(c) 20 m2

(d) m2

ANSWER : (a) 12 m2

16. The ratio of the areas of two squares one having double its diagonal than the other is:

(a) 2:1

(b) 3:1

(c) 3:2

(d) 4:1

ANSWER : (d) 4:1

17. The length of a plot is four times its breadth. A playground measuring 1200 square metres

occupies a third of the total area of the plot. What is the lengthof the plot in metres?

(a) 20

(b) 30

(c) 60

(d) none of these

ANSWER : (d) none of these

18. The area of a rectangle 144 m long is the same as that of a square having a side 84 m long.

The width of the rectangle is:

(a) 7 m

(b) 14 m

(c) 49 m

(d) cannot be determined

ANSWER : (c) 49 m

19. The length and breadth of a rectangular piece of land are in ratio of 5:3. The owner spent Rs.

3000 for surrounding it from all the sides at Rs. 7.50 per metre. The difference between its

length and breadth is:

(a) 50 m

(b) 100 m

(c) 150 m

(d) 200 m

ANSWER : (a) 50 m

20. A verandah 40 metres long 15 metres broad is to be paved with stones each measuring 6

dm by 5 dm. the number of stones required is:

(a) 1000

(b) 2000

(c) 3000

(d) none of these

ANSWER : (b) 2000

21. Area of four walls of a room is 77 square metres. The length and breadth of the room are 7.5

metres and 3.5 metres respectively. The height of the room is:

(a) 3.5 metres

(b) 5.4 metres

(c) 5.4 metres

(d) 7.7 metres

ANSWER : (a) 3.5 metres

22. The length of rectangular room is 4 metres. If it can be partitioned into two equal square

rooms, what is the length of each partition in metres?

(a) 1

(b) 2

(c) 4

(d) data inadequate

ANSWER : (b)2

23. Of the two square fields the area of the one is 1 hectare, while the another one is broader by

1%. The difference in areas is:

(a) 101 sq. metres

(b) 201 sq. metres

(c) 100 sq. metres

(d) 200 sq. metres

ANSWER : (b) 201 sq. metres

24. The cost of carpeting a room 15 metres long with a carpet 75 cm wide at 30 paise per metre

is Rs. 36. The breadth of the room is:

(a) 6 metres

(b) 8 metres

(c) 9 metres

(d) 12 metres

ANSWER : (a) 6 metres

25. If the length of diagonal AC of a square ABCD is 5.2 cm, then area of the square ABCD is:

(a) 15.12 sq. cm

(b) 13.52 sq. cm

(c) 12.62 sq. cm

(d) 10 sq. cm

ANSWER : (b) 13.52 sq. cm

26. The length and breadth of a playground are 36 m and 21 m respectively Flagstaffs are

required to be fixed on all along the boundary at 3 distance of 3 m apart. The number of

flagstaffs will be:

(a) 37

(b) 38

(c) 39

(d) 40

ANSWER : (b) 38

27. If the side of a square be increased by 4 cms, the area increases by 60 sq. cms. The side of

the square is:

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) none of these

ANSWER : (d) none of these

28. A rectangular lawn 60 metres by 40 metres have two road each 5 metres wide running in

the middle of it one parallel to length and the other parallel to breadth. The cost of

gravelling the roads at 60 paise per sq. metre is:

(a) Rs 300

(b) Rs 280

(c) Rs.285

(d) Rs.250

ANSWER : (c) Rs.285

29. The ratio between the length and breadth of a rectangular field is 5:4, the breadth is 20

metres less than the length, the perimeter of the field is:

(a) 260 m

(b) 280 m

(c) 360 m

(d) none of these

ANSWER : (c) 360 m

30. A rectangular plot is half as long again as it is broad. The area of the lawn is (2/3) hectares.

The length of the plot is:

(a) 100 metres

(b) 66.66 metres

(c) 33 metres

(d) 120 metres

ANSWER : (a) 100 metres

31. An error 2% in excess is made while measuring the side of a square. What is the percentage

of error in the calculated area of the square?

(a) 4.04 %

(b) 2.02 %

(c) 4 %

(d) 2 %

Answer : (a) 4.04%

32. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the

middle of the park and rest of the park has been used as a lawn. The area of the lawn is

2109 sq. m. what is the width of the road?

(a) 5 m

(b) 4 m

(c) 2 m

(d) 3 m

Answer : (d) 3m

33. A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the

percentage of decrease in area?

(a) 30 %

(b) 28 %

(c) 32 %

(d) 26 %

Answer : (b) 28 %

34. If the length of a rectangle is halved and its breadth is tripled, what is the percentage change

in its area?

(a) 25 % Increase

(b) 25 % Decrease

(c) 50 % Decrease

(d) 50 % Increase

Answer : (d) 50 % Increase

35. A person walked diagonally across a square plot. Approximately, what was the percent

saved by not walking along the edges?

(a) 35%

(b) 30 %

(c) 20 %

(d) 25%

Answer : (b) 30 %

36. A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the

area of the field is 680 sq. feet, how many feet of fencing will be required?

(a) 95

(b) 92

(c) 88

(d) 82

Answer : (c) 88

37. A rectangular parking space is marked out by painting three of its sides. If the length of the

unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out

the area of the parking space in square feet?

(a) 126 sq. ft.

(b) 64 sq. ft.

(c) 100 sq. ft.

(d) 140 sq. ft.

Answer : (a) 126 sq. ft.

38. The area of a rectangle plot is 460 square metres. If the length is 15% more than the

breadth, what is the breadth of the plot?

(a) 14 metres

(b) 20 metres

(c) 18 metres

(d) 12 metres

Answer : (b) 20 metres

39. A large field of 700 hectares is divided into two parts. The difference of the areas of the two

parts is one-fifth of the average of the two areas. What is the area of the smaller part in

hectares?

(a) 400

(b) 365

(c) 385

(d) 315

Answer : (d) 315

40. The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by

slabs at the rate of Rs. 800 per sq. metre.

(a) Rs.12000

(b) Rs.19500

(c) Rs.18000

Answer: (d) 18000

41. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth

is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of

the rectangle?

(a) 18 cm

(b) 16 cm

(c) 40 cm

(d) 20 cm

Answer : (c) 40 cm

42. . If a square and a rhombus stand on the same base, then what is the ratio of the areas of the

square and the rhombus?

(a) equal to ½

(b) equal to ¾

(c) greater than 1

(d) equal to 1

Answer : (d) equal to 1

43. The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m,

find out the area of the field.

(a) 37500 m2

(b) 30500 m2

(c) 32500 m2

(d) 40000 m2

Answer : (a) 37500 m2

44. A room 5m 44cm long and 3m 74cm broad needs to be paved with square tiles. What will be

the least number of square tiles required to cover the floor?

(a) 176

(b) 124

(c) 224

(d) 186

Answer : (a) 176

45. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the

plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

(a) 60 m

(b) 100 m

(c) 75 m

(d) 50 m

Answer : (a) 60 m

46. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling

along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes,

then what is the area of the park (in sq. m)?

(a) 142000

(b) 112800

(c) 142500

(d) 153600

Answer : (d) 153600

47. What is the percentage increase in the area of a rectangle, if each of its sides is increased by

20%?

(a) 45%

(b) 44%

(c) 40%

(d) 42%

Answer : (b) 44 %

48. If the difference between the length and breadth of a rectangle is 23 m and its perimeter is

206 m, what is its area?

(a) 2800 m2

(b) 2740 m2

(c) 2520 m2

(d) 2200 m2

Answer : (C) 2520 m2

49. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? (a) 16 cm (b) 18 cm (c) 14 cm (d) 20 cm

Answer : (b) 18 cm

50. What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? (a) 814 (b) 802 (c) 836 (d) 900

Answer : (a) 814

51. The diagonal of the floor of a rectangular room is 712 feet. The shorter side of the room is 4 12 feet. What is the area of the room? (a) 27 square feet (b) 22 square feet (c) 24 square feet (d) 20 square feet

Answer : (a) 27 square feet

52. A tank is 25 m long, 12 m wide and 6 m deep. What is the cost of plastering of its walls and bottom at the rate of 75 paise per sq. m? (a) Rs. 558 (b) Rs. 502 (c) Rs. 516 (d) Rs. 612

Answer : (a) Rs. 558

53. The diagonal of a rectangle is 41−−√ cm and its area is 20 sq. cm. What is the perimeter of the rectangle? (a) 16 cm (b) 10 cm (c) 12 cm (d) 18 cm

Answer : (d) 18 cm

54. It is decided to construct a 2 metre broad pathway around a rectangular plot on the inside. If the area of the plots is 96 sq.m. and the rate of construction is Rs. 50 per square metre., what will be the total cost of the construction? (a) Rs.3500 (b) Rs. 4200 (c) Insufficient Data (d) Rs. 4400

Answer : (c) Insufficient Data

55. The area of a parallelogram is 72 cm2 and its altitude is twice the corresponding base. What is the length of the base? (a) 6 cm (b) 7 cm (c) 8 cm (d) 12 cm

Answer : (a) 6 cm

56. Two diagonals of a rhombus are 72 cm and 30 cm respectively. What is its perimeter? (a) 136 cm (b) 156 cm (c) 144 cm (d) 121 cm

Answer : (b) 156 cm

57. The base of a parallelogram is (p + 4), altitude to the base is (p - 3) and the area is (p2 - 4), find out its actual area. (a) 40 sq. units (b) 54 sq. units (c) 36 sq. units

(d) 60 sq. units

Answer : (d) 60 sq. units

58. A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle? (a) 1443√−48π cm2 (b) 1443√−36π cm2 (c) 1213√−36π cm2 (d) 1213√−48π cm2

Answer : (a) 1443√−48π cm2

59. A rectangular plot measuring 90 metres by 50 metres needs to be enclosed by wire fencing such that poles of the fence will be kept 5 metres apart. How many poles will be needed? (a) 30 (b) 44 (c) 56 (d) 60

Answer : (c) 56

60. If the diagonals of a rhombus are 24 cm and 10 cm, what will be its perimeter (a) 42 cm (b) 64 cm (c) 56 cm (d) 52 cm

Answer : (d) 52 cm