Area problems
- 1. 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?
Options- A. 7 m
- B. 14 m
- C. 49 m
- D. Cannot be determined Discuss
Correct Answer: 49 m
Explanation:
Area of the square = (84 + 84) m2
Area of the rectangle = (144 x width) m2
From question both area would be same,
? Width = (84 x 84) / 144 m = 49 m
- 2. The length of a plot is four times its breath. A playground measuring 1200 square meters occupies one third of the total area of a plot . what is the length of the plot in meters?
Options- A. 20
- B. 30
- C. 60
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Area of the plot = (3 x 1200) m2
= 3600 m2
Let breadth = y meters
Then Length = 4y meters,
Now area = 4y x y = 3600 m2
? y2 = 900 m2
? y = 30 m
? Length of plot = 4y m
= (4 x 30) m
=120 m
- 3. The cost of papering the four walls of a room is Rs. 48. Each one of length, breadth and height of another room is double that of this room.The cost of papering the walls of the new room is?
Options- A. Rs. 384
- B. Rs. 298
- C. Rs. 192
- D. Rs. 96 Discuss
Correct Answer: Rs. 192
Explanation:
Let the length, breadth and height of the room be l, b and h respectively
As per question
Cost of 2(l + b) x h = Rs. 48
? Required cost = cost of 2 (2l + 2b) x 2h
= cost of 4 [2(l + b) x h ]
= 4 x Rs. 48
= Rs. 192
- 4. Area of a four walls a room is 168 Sq. meters . The breadth and height of a room are 8 meters and 6 meters respectively . The length of the room is?
Options- A. 14 meters
- B. 12 meters
- C. 6 meters
- D. 3.5 meters Discuss
Correct Answer: 6 meters
Explanation:
Area of a four walls = 2(l + 8) x 6 = 168m2
? (l + 8) = 14
? l = 14-8
= 6 meters
- 5. Area of a four wall of a room is 77 square meters . the length and breadth of room are 7.5 meters and 3.5 meters respectively . the height of the room is?
Options- A. 3.5 meters
- B. 5.4 meters
- C. 6.77 meters
- D. 7.7 meters Discuss
Correct Answer: 3.5 meters
Explanation:
Area of four walls = 2 x (l + b ) x h
? 2 x (7.5 + 3.5 ) x h = 77 m2
? h = 77 / (2 x 11) = 7/2
? h = 3.5 meters
- 6. A rectangle has 15 cm as its length and 150 cm 2 as its area .Its area is increased to 1 1 / 3 times the original area by increasing only its length . Its new perimeter is?
Options- A. 50 cm
- B. 60 cm
- C. 70 cm
- D. 80 cm Discuss
Correct Answer: 60 cm
Explanation:
Breadth of the rectangle = (150/15) cm
= 10 cm
New area = (4/3 x 150) cm2
= 200 cm2
New length = 200/10 cm
=20 cm
New perimeters = 2(20 + 10) cm
= 60 cm
- 7. The length of a rectangle room is 4 meters . if it can be partitioned into two equal square rooms . what is the length of each partition in meters?
Options- A. 1
- B. 2
- C. 4
- D. Data inadequate Discuss
Correct Answer: 2
Explanation:
Let the width of the room be x members
Then, its area = (4x) m2
Area of each new square room = (2x)m2
Let the side of each new room = y meters
Then, y2 = 2x
Clearly, 2x is a complete square when x=2
? y2 = 4
? y = 2 m .
- 8. The length and breadth of a square are increased by 40% and 30% respectively. The area of a resulting rectangle exceeds the area of the square by?
Options- A. 42%
- B. 62%
- C. 82%
- D. None of these Discuss
Correct Answer: 82%
Explanation:
Let the side of the square = 100 m
So area of square = 100 x 100 = 10000.
New length = 140 m,
New breadth = 130 m
Increase in area = [(140 x 130) - (100 x 100)] m2
= 8200 m2
? Required increase percent = (8200/ 10000) x 100 % = 82%
- 9. 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 3.50 per sq. meter is?
Options- A. Rs. 500
- B. Rs. 600
- C. Rs. 700
- D. Rs. 800 Discuss
Correct Answer: Rs. 700
Explanation:
Area of verandah = [(25 x 20) -(20 x 15)] m2
= 200 m2
? Cost of flooring = Rs. (200 x 3.50)
= Rs. 700
- 10. Of the square fields the area of the one is 1 hectare, while the another one is broader by 1% the difference is area is?
Options- A. 101 sq. metres
- B. 201 sq. metres
- C. 100 sq. metres
- D. 200 sq. metres Discuss
Correct Answer: 201 sq. metres
Explanation:
Area of the square field = 1 hectare
= 10000 m2
Side of the square = ? 10000 m = 100 m
Side of another square field = 100 + 1 = 101 m
? Required difference of area
= [(101)2 - (100)2] m2
=[(101 + 100 ) (101 - 100) ] m2
= 201 m2
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