Question

In the figure PSR, RTQ and PAQ are 3 semicircles of diameters $10cm,3cmand7cm$ respectively. Find the perimeter of the shaded region.

Answer 1

Radius of semicircle $PSR=\frac{1}{2}\times 10=5cm$

Radius of semicircle $RTQ=\frac{1}{2}\times 3cm=1.5cm$

Radius of semicircle $PAQ=\frac{1}{2}\times 7=3.5cm$

Perimeter of shaded region $=$ Circumference of semicircle $PSR+$ Circumference of semicircle $RTQ+$ Circumference of semicircle $PAQ$

Threfore,

Perimeter of shaded region $=\pi \times 5+\pi \times 1.5+\pi \times 3.5=10\pi =31.4$