Area problems
- 1. 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?
Options- A. 814
- B. 820
- C. 840
- D. 844 Discuss
Correct Answer: 814
Explanation:
Area of each tile = (41 x 41) cm2.
| ∴ Required number of tiles = | ❨ | 1517 x 902 | ❩ | = 814. |
| 41 x 41 |
- 2. 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?
Options- A. 16 cm
- B. 18 cm
- C. 24 cm
- D. Data inadequate
- E. None of these Discuss
Correct Answer: 18 cm
Explanation:
| 2(l + b) | = | 5 |
| b | 1 |
⟹ 2l + 2b = 5b
⟹ 3b = 2l
| b = | 2 | l |
| 3 |
Then, Area = 216 cm2
⟹ l x b = 216
| ⟹l x | 2 | l | = 216 |
| 3 |
⟹ l2 = 324
⟹ l = 18 cm.
- 3. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options- A. 1520 m2
- B. 2420 m2
- C. 2480 m2
- D. 2520 m2 Discuss
Correct Answer: 2520 m2
Explanation:
Solving the two equations, we get: l = 63 and b = 40.
∴ Area = (l x b) = (63 x 40) m2 = 2520 m2.
- 4. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
Options- A. Rs. 456
- B. Rs. 458
- C. Rs. 558
- D. Rs. 568 Discuss
Correct Answer: Rs. 558
Explanation:
| Area to be plastered | = [2(l + b) x h] + (l x b) |
| = {[2(25 + 12) x 6] + (25 x 12)} m2 | |
| = (444 + 300) m2 | |
| = 744 m2. |
| ∴ Cost of plastering = Rs. | ❨ | 744 x | 75 | ❩ | = Rs. 558. |
| 100 |
- 5. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Options- A. 40%
- B. 42%
- C. 44%
- D. 46% Discuss
Correct Answer: 44%
Explanation:
Original area = (xy) m2.
| New length = | ❨ | 120 | x | ❩m | = | ❨ | 6 | x | ❩m. |
| 100 | 5 |
| New breadth = | ❨ | 120 | y | ❩m | = | ❨ | 6 | y | ❩m. |
| 100 | 5 |
| New Area = | ❨ | 6 | x x | 6 | y | ❩m2 | = | ❨ | 36 | xy | ❩m2. |
| 5 | 5 | 25 |
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
| ∴ Increase % = | ❨ | 11 | xy x | 1 | x 100 | ❩% | = 44%. |
| 25 | xy |
- 6. Area of a square is 1/2 hectare. The diagonal of the square is?
Options- A. 250 meter
- B. 100 meter
- C. 50? 2 meter
- D. 50 meter Discuss
Correct Answer: 100 meter
Explanation:
Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2
Again Area = 1/2 x (Diagonal)2
So 1/2 x (Diagonal)2 = 5000m2
? Diagonal2= 10000
? Diagonal = 100
- 7. The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be?
Options- A. 25m2
- B. 28 m2
- C. 30m2
- D. None of these Discuss
Correct Answer: 30m2
Explanation:
Altitude = ?(13)2 - (5)2
= ?144 = 12m
? Area of the triangle = (5 x 12 ) / 2 m2
= 30m2
- 8. The length of a rectangle is double while its breadth is halved. What is the percentage change in area?
Options- A. 50
- B. 75
- C. No change
- D. None of these Discuss
Correct Answer: No change
Explanation:
Let length = l and breadth = b
Then, area = lb
New length = 2l
And new breadth = b/2
? New area = ( 2l ) x (b/2) = lb
So, there is no change in area .
- 9. The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is?
Options- A. 6 meters
- B. 8 meters
- C. 9 meters
- D. 12 meters Discuss
Correct Answer: 6 meters
Explanation:
Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
? Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
- 10. If the side of a square is increased by 25%, then how much percent does its area get increased?
Options- A. 125
- B. 156.25
- C. 50
- D. 56.25 Discuss
Correct Answer: 56.25
Explanation:
Let area 100 m2
Then, side = 10 m
New side = 125 % of 10
= (125/100) x 10
= 12.5 m
New area = 12.5 x 12.5 m2
=(12.5)2 sq. m
? Increase in area = (12.5)2 - (10)2 m2
= 22.5 x 2.5 m2
=56.25 m2
% Increase = 56.25 %
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