Question

Find the perimeter and area of the shaded region in the following figure:

Answer 1

R.E.F image

Circumference of bigger semi-circle $=2\pi R=2\times \frac{22}{7}\times 14=88cm$

Circumference of smaller semi-circle $=2\pi r=2\times \frac{22}{7}\times 7=44cm$

Perimeter $=88+44+2x=132+2\times 7=132+14=146cm$

Area of bigger semi-circle $=\frac{\pi R^2}{2}=\frac{22\times 14\times 14}{7\times 2}=308c{m}^2$

Area of smaller semi-circle $=\frac{\pi r^2}{2}=\frac{22\times 7\times 7}{7\times 2}=77c{m}^2$

Area of shaded region = Area of big - Area of small

$=308-77=231c{m}^2$