Question

The diagram given below shows paths drawn inside a rectangular field 50 m long and 35 m wide. The width of each path is 5 meters. Find the area of the shaded portion.

Answer 1

Hint: To find the area of the shaded region, first, we will have to calculate the area of the rectangular field, then the area of the unshaded portion. But the unshaded portion consists of 4 smaller rectangular regions, so in order to calculate the area of the unshaded portion, we will have to calculate the area of four smaller rectangular regions. After all these, area of shaded portion = area of the rectangular field – an area of the unshaded portion.

 Complete step by step answer:
Here we have, length of rectangular field = 50 m and width of rectangular field = 35 m
So, we can find the area of rectangular region as length $\times $ width
$\therefore $ Area of rectangular field = length $\times $ width
= 50 m $\times $35 m
= 1750 ${{m}^{2}}$
Since, width of shaded portion = 5 m
Now, we have, length of smaller rectangular region $=\dfrac{50-5}{2}m=\dfrac{45}{2}m$ and
Width of smaller rectangular region $=\dfrac{35-5}{2}m$ $=\dfrac{30}{2}m=15m$
Here, also we can find the area of smaller rectangular region as length $\times $ width
$\therefore $ Area of smaller rectangular region = length $\times $ width
= 15 m $\times $ $\dfrac{45}{2}$ m
= 337.5 ${{m}^{2}}$
Area of unshaded portion = 4 $\times $ Area of smaller rectangular region
= 4 $\times $ 337.5 ${{m}^{2}}$
= 1350 ${{m}^{2}}$
Area of shaded portion = Area of rectangular field – Area of unshaded portion
= 1750 ${{m}^{2}}$ $-$ 1350${{m}^{2}}$
= 400 ${{m}^{2}}$
Hence, area of shaded portion = 400 ${{m}^{2}}$

Note:
 Remember before finding the area of the region, we must observe the shape of the region like if it is of the form of a rectangle, square circle, or other geometrical shapes, accordingly we have to apply the formula to find the area of the required region.