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 = r_{1}

Diameter of semicircle RTQ = 3 cm

⇒ Radius of semicircle RTQ = = 1.5 cm = r_{2}

Diameter of semicircle PAQ = 7 cm

⇒ Radius of semicircle PAQ = = 3.5 cm = r_{3}

∵ Perimeter of semicircle = πr

∴ Perimeter of semicircle PSR = πr_{1}

= 3.14 × 5 = 15.7 cm

Similarly, Perimeter of semicircle RTQ = πr_{2}

= 3.14 × 1.5 = 4.71 cm

and Perimeter of semicircle PAQ = πr_{3}

= 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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