# Area - Aptitude Questions and Answers - RejinpaulPlacement

@ : Home > Arithmetic Aptitude > Area > Level - 1

### Quick Links

1.
One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
Answer & Solution
Answer: (C) 120 m2

Solution: Other side = √(〖(17)〗^2-〖 (15)〗^2 ) = √(289-225) = √64 = 8 m.

Area = (15 * 8) m2 = 120 m2 .

2.
A lawn is in the form of a rectangular having its sides in the ratio 2 : 3. The area of the lawn is 1/6 hectares. Find the length and breadth of the lawn.
Answer & Solution
Answer: c) 33 1/3 m, 50 m

Solution: Let length = 2x metres and breadth = 3x metres.

Now, area = [ 1/6 * 1000] m2 =( 5000/3 ) m2.

So, 2x * 3x = ( 5000/3 )

=> x2 = ( 2500/9 )
x = 50/3

Length = 2x = 100/3 m = 33 1/3 m and Breadth = 3x = [3 * 50/3 ] m = 50 m.
3.
Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs. 12.40 per square metre..
Answer & Solution
Answer: c) Rs. 1934.40

Solution: Area of the carpet = Area of the room = [13 * 9] m2 = 117 m2.

Length of the carpet = ( Area/Width ) = [117 * 4/3 ] = m = 156 m

Cost of carpeting = Rs. (156 * 12.40) = Rs. 1934.40
4.
.If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
Answer & Solution
Answer: (d) 120 cm2

Solution: Let length = x and breadth = y. Then,

2 (x + y) = 46

=> x + y = 23 and x2 + y2 = (17)2 = 289

Now, (x + y)2 = (23)2

=> (x2 + y2) = (23)2

=> (x2 + y2) + 2xy = 529

=> 289 + 2xy = 529

=> xy = 120

Area = xy = 120 cm2.

5.
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. Find the length of the rectangle.?
Answer & Solution
Answer: b) 20 cm

Solution: Let breadth = x. Then, length = 2x. Then,

(2x – 5) (x + 5) – 2x * x = 75

=> 5x – 25 = 75

=> x = 20

Length of the rectangle = 20 cm.

6.
In measuring the sides of a rectangle, one side is taken 5 % in excess, and the other 4 % in deficit. Find the error percent in the area calculated from these measurements
Answer & Solution
Answer: c) 0.8 %

Solution: Let x and y be the sides of the rectangle. Then, Correct area = xy.

Calculated area = (105/100 x ) * (96/100 y) = (504/500 xy)

Error in measurement = (504/500 xy) - xy = 4/500 xy

Error % = [4/500 xy * 1/xy * 100] % = 4/5 % = 0.8 %

7.
A rectangular grassy plot 110 m by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre.
Answer & Solution
Answer: (d) Rs. 680

Solution: Area of the plot = (110 * 65) m2 = 7150 m2.

Area of the plot excluding the path = [(110 – 5) * (65 – 5)] m2 = 6300 m2.

Area of the path = (7150 – 6300) m2 = 850 m2.

Cost of gravelling the path = Rs. [850 * 80/100 ] = Rs. 680