A rectangular lawn, 75 m by 60 m, has two roads, each road 4 m wide, running through the middle of the lawn,

Question:

A rectangular lawn, 75 m by 60 m, has two roads, each road 4 m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at Rs 50 per m2.

Solution:

Area of rectangle ABCD = Length × Breath
= 75 × 4
= 300 m2

Area of rectangle PQRS = Length × Breath
= 60 × 4
= 240 m2

Area of square EFGH = (side)2
= (4)2
= 16 m2

∴ Area of the footpath = Area of rectangle ABCD + Area of rectangle PQRS − Area of square EFGH
 = 300 + 240 − 16
 = 524 m2

The cost of gravelling the road per m2 = Rs 50
The cost of gravelling the roads 524 m2 = Rs 50 × 524
= Rs 26200

Hence, the total cost of gravelling the roads at Rs 50 per m2 is Rs 26200.

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