Question

In the given figure ABCD is a rectangle. It consists of a circle and two semi circles each of which are of radius $5$cm. Find the area of the shaded region. Give your answer correct to three significant figures.

Answer 1

As we can see from the figure

length of rectangle=$4\times$ radius of circle $=4\times 5$cm$=20$ cm

breadth of rectangle=$2\times$ radius of circle $=2\times 5$cm$=10$cm

hence required area$=$ area of rectangle - (area of semicircle +$2\times$ area of semicircle)

$=20\times 10$-{$\left(\pi \right)\times \left(5^2\right)$+$2\times \frac{1}{2}\times \left(\pi \right)\times \left(5^2\right)$}$c{m}^2$

$=$$(200-157)$ $c{m}^2$

$=$ $43$ $c{m}^2$