Question

A 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs 40 per m².

Answer 1

The length and breadth of the lawn are 80 m and 64 m, respectively.
The layout of the roads is shown in the figure below:

Area of the road ABCD = $80\times 5=400{\mathrm{m}}^2$
Area of the road PQRS = $64\times 5=320{\mathrm{m}}^2$
Clearly, the area EFGH is common in both the roads.
Area EFGH = $5\times 5=25{\mathrm{m}}^2$
Area of the roads = $400+320-25$
= $695{\mathrm{m}}^2$
Given:
Cost of gravelling 1 m² area = Rs 40
∴ Cost of gravelling 695 m² area = $695\times 40$
= Rs 27,800