Question

The adjacent figure consists of four small semi-circles of equal radii and big semi-circles of equal radii (each $21cm$). Find the area of the shaded region.

Answer 1

Radius of big semicircle $=21cm$

Area of shaded part = Area of two big semicircles- Area of 2 small semicircle + Area of 2 small semicircles

= 2$\times$ Area of bigger semicircle

( Visualise this by rejoining the smaller semicircle into unshaded part of bigger semicircle )

$=\frac{2\times \pi \times r^2}{2}=\pi \times (21{)}^2=441\pi c{m}^2$