Question

A rectangular lawn 75 m by 60 m, has two roads each 4 m wide running through the middle of the lawn one parallel to the length and other parallel to breadth as shown in figure 9.12. Find the cost of gravelling the roads at Rs. 4.50 per sq.m.

Answer 1

Length of the rectangle ABCD = BC = 75 m
Breadth of the rectangle = AB = 4 m
Area of the rectangle = BC × AB
= 75 m × 4 m
= 300 m²

Length of the rectangle EFGH = EF = 60 m
Breadth of the rectangle = EH = 4 m
Area of the rectangle = EF × EH
= 60 m × 4 m
= 240 m²

Length of the rectangle PQRS = QR = 4 m
Breadth of the rectangle = PQ = 4 m
Area of the rectangle = QR × PQ
= 4 m × 4 m
= 16 m²

Now, area of the road = area of ABCD + area of EFGH − area of PQRS
= (300 + 240 – 16) m²
= 524 m²
Cost of gravelling the road for 1 m² = Rs 4.50
∴ Cost of gravelling the road for 524 m² = Rs 4.50 × 524 = Rs 2358