PS is diameter of a circle of diameter 21 cm.  In the diameter PS, Q and R are points such that PQ, QR, RS are all equal.  Semi-circles are drawn on PQ and QS as diameter.  What is the perimeter of shaded region?

66 cm

PQ = 7 cm

QS = 14 cm

⇒ perimeter of region with diameter PQ = \(\pi \)r = \(\pi \) \(\frac{PQ}{2}\) = \(\frac{22}{7}\) × \(\frac{7}{2}\) = 11 cm

⇒ perimeter of region with diameter QS = \(\pi \)r" = \(\pi \) \(\frac{QS}{2}\) = \(\frac{22}{7}\) × \(\frac{14}{2}\) = 22 cm

⇒ perimeter of region with diameter PS = \(\pi \)r' = \(\pi \) \(\frac{PS}{2}\) = \(\frac{22}{7}\) × \(\frac{21}{2}\) = 33 cm

Total Perimeter = 11 + 22 + 33 = 66 cm