Question

An $80m$ by $64m$ rectangular lawn has two roads, each $5m$ 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 $Rs.24$ per $m^2.$

Answer 1

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

Area of the road $ABCD=80\times 5=400m^2$ [$\because$ Area of rectangle $=l\times b$]
Area of the road $PQRS=64\times 5=320m^2$
Clearly, the area $EFGH$ is common in both the roads.
Area $EFGH=5\times 5=25m^2$
Area of the roads $=400+320-25=695m^2$

It is given that,
Cost of gravelling $1m^2$ area $=Rs.24$
$\therefore$ Cost of gravelling $695m^2$ area $=695\times 24=Rs.16680$