Q. 384.0( 15 Votes )

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.


Answer :

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.


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