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 graveling the roads at $$\text{Rs }40$$ per$$\text{ m}^2$$.

Answer 1

Length of rectangular lawn = 80 m
Breadth = 64 m
Width of road = 5 m
Area of horizontal road $$= 5 \times 80 = 400\,\text{m}^2 $$
Area of vertical road $$= 5 \times 64 = 320\,\text{m}^2$$
Area of common part to both roads $$= 5 \times 5 = 25\,\text{m}^2$$
Now,
Area of roads to be gravelled $$=$$ Area of horizontal road $$+$$ Area of vertical road $$-$$ Area of common part to
both roads
$$= 400 + 320 - 25$$
$$= 695 \text{ m}^2$$
Therefore, Area of roads to be gravelled is $$695\,\text{m}^2$$
Cost of gravelling $$= 695 \times\ 40 = \text{Rs}\,27800$$