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.
Given:
Diameter of semicircle PSR = 10 cm
⇒ Radius of semicircle PSR = 
= 5 cm = r1
Diameter of semicircle RTQ = 3 cm
⇒ Radius of semicircle RTQ = 
= 1.5 cm = r2
Diameter of semicircle PAQ = 7 cm
⇒ Radius of semicircle PAQ = 
= 3.5 cm = r3
∵ Perimeter of semicircle = πr
∴ Perimeter of semicircle PSR = πr1
= 3.14 × 5 = 15.7 cm
Similarly, Perimeter of semicircle RTQ = πr2
= 3.14 × 1.5 = 4.71 cm
and Perimeter of semicircle PAQ = πr3
= 3.14 × 3.5 = 10.99 cm
Perimeter of shaded region = Perimeter of semicircle PSR
+ Perimeter of semicircle RTQ
+ Perimeter of semicircle PAQ
= 15.7 + 4.71 + 10.99 = 31.4 cm
Hence, the perimeter of the shaded region is 31.4 cm.