Question

In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π= 3.14] [CBSE 2014]

Answer 1

Perimeter of shaded region = Length of the arc PAQ + Length of the arc PSR + Length of the arc RTQ
$$\begin{gathered} =\frac{1}{2}\times 2\mathrm{\pi }{r}_1+\frac{1}{2}\times 2\mathrm{\pi }{r}_2+\frac{1}{2}\times 2\mathrm{\pi }{r}_3 \\ =\frac{1}{2}\times 2\mathrm{\pi }\left(\frac{7}{2}\right)+\frac{1}{2}\times 2\mathrm{\pi }\left(\frac{10}{2}\right)+\frac{1}{2}\times 2\mathrm{\pi }\left(\frac{3}{2}\right) \\ =\frac{7}{2}\mathrm{\pi }+5\mathrm{\pi }+\frac{3}{2}\mathrm{\pi } \\ =\frac{7}{2}\mathrm{\pi }+\frac{3}{2}\mathrm{\pi }+5\mathrm{\pi } \\ =5\mathrm{\pi }+5\mathrm{\pi } \\ =10\mathrm{\pi } \\ =31.4\mathrm{cm} \end{gathered}$$
Hence, the perimeter of shaded region is 31.4 cm.