Area with Explanation

Q8. A rectangular park 55 m x 35 m has two roads each 4 meters wide running in the middle of it, One parallel to the length and the other parallel to the breadth. If the rate of gravelling the road is 75 paisa per sq.m, find the cost of gravelling the road?

Answer- Option B

Explanation-

Area of crossroads = (55 x 4 + 35 x 4 - 4 x 4) m² = 344 m².
Cost of gravellling = Rs.

344 *

75 100

= Rs. 258.

Q9. One meter broad boundary is to be gardened around a rectangular home having a perimeter equal to 340 m. If the rate of gardening is Rs. 10 per sq.m, find the cost of gardening the boundary?

Answer- Option C

Explanation-

Given 2(l + b) = 340
Area of the boundary = [(l + 2) (b + 2) - lb] = 2(l + b) + 4 = 344.
Cost of gravellling = Rs. (344 x 10) = Rs. 3440.

Q10. The difference between the area of a rectangle and a square is 100 sq.cm, and their perimeter is equal to 80 cm. What are the sites of the rectangle?

Answer- Option D

Explanation-

Side of the square =

80 4

cm = 20 cm.

2(l + b) = 80
l + b = 40. Now, (20 x 20) - lb = 100
lb = 300.

(l - b) =   (l + b)² - 4lb =   (40 x 40) - (4 x 300) = 20.

Now, l + b = 40 and l - b = 20
l = 30 and b = 10.
Sides of the rectangle are 30 cm and 10 cm.

Q11. Rakesh is running at a rate of 4 km/hr passes a square loan diagonally in 3 minutes. The area of the loan is?

Answer- Option A

Explanation-

Speed of Rakesh =

4 x

5 18

m/sec =

10 9

m/s.

Time taken = (3 x 60) sec = 180 sec
Length of diagonal = (speed x time)
=

10 9

x 180

m = 200 m.

Area of the field =

1 2

x (diagonal)²

=

1 2

x 200 x 200

m² = 20000 m²

Q12. The floor of a square room is to be paved with granite slabs having dimensions 20 cm x 30 cm. If the side of a room is 3 m, find the number of slabs required?

Answer- Option C

Explanation-

Number of slabs =

300 x 300 20 x 20

= 225.

Q13. The length of a rectangle is 20% more than its breadth. Find the ratio of the area of the rectangle to that of the square whose side is equal to the breadth of the rectangle?

Answer- Option B

Explanation-

Let breadth be x metres. Then, length = 120% of x =

6 5

x m

Required ratio =

6x 5

* x *

1 x*x

= 6 : 5

Q14. One side of a right-angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is

Answer- Option A

Explanation-

Let the sides be acm and 2acm
Then, a² + (2a)² = 10²
a² = 20
Area =

1 2

x a x 2a = a² = 20cm²