Question

Find the area of shaded design in the given figure, where $ABCD$ is a square of side $10cm$ and semi-circles are drawn with each of the side as diameter. (Take $\pi =3.14$)

Answer 1

Let us mark the four unshaded regions as $I,II,III$ and $IV$

Area of $1$ + Area of $III$

= Area of $ABCD-$ Area of two semicircles of radius $5cm$ each

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

$=(100-3.14\times 25)c{m}^2=(100-78.5)c{m}^2=21.5c{m}^2$

Similarly, Area of $II$ + Area of $IV$ $=21.5c{m}^2$

So, Area of the shaded design

= Area of $ABCD-$ Area of $(I+II+III+IV)$

$=(100-2\times 21.5)c{m}^2$

$=(100-{43}_{}c{m}^2=57c{m}^2$