Question

A rectangular lawn, 75m by 60m, has two roads, each road 4m 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 ₹ 50 per m².

Answer 1

We know that for the road ABCD

It is given that length = 75m and breadth = 4m

We know that

Area of road ABCD = l × b

By substituting the values

Area of road ABCD = 75 × 4

So we get

Area of road ABCD = 300 m²

We know that for the road PQRS

It is given that length = 60m and breadth = 4m

We know that

Area of road PQRS = l × b

By substituting the values

Area of road PQRS = 60 × 4

So we get

Area of road PQRS = 240 m²

We know that for road EFGH

It is given that side = 4m

Area of road EFGH = side²

By substituting the value

Area of road EFGH = 4² = 16 m²

The total area of the road for gravelling = Area of road ABCD + Area of road PQRS – Area of road EFGH

By substituting the values

Total area of the road for gravelling = 300 + 340 – 16

So we get

Total area of the road for gravelling = 524 m²

It is given that the cost of gravelling the road = ₹ 50 per m²

So the cost of gravelling 524 m² road = ₹ (50 × 524) = ₹ 26200

Therefore, the cost of gravelling the road is ₹ 26200.