Question

In the the following figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.

Answer 1

Perimeter of shaded region = Length of the arc PAQ + Length of the arc PSR + Length of the arc RTQ

\[= \frac{1}{2} \times 2\pi r_1 + \frac{1}{2} \times 2\pi r_2 + \frac{1}{2} \times 2\pi r_3 \]
\[ = \frac{1}{2} \times 2\pi\left( \frac{7}{2} \right) + \frac{1}{2} \times 2\pi\left( \frac{10}{2} \right) + \frac{1}{2} \times 2\pi\left( \frac{3}{2} \right)\]
\[ = \frac{7}{2}\pi + 5\pi + \frac{3}{2}\pi\]
\[ = 10\pi\]
\[ = 31 . 4 cm\]

Hence, the perimeter of shaded region is 31.4 cm.