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Answer:
Perimeter is 66cm
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Solution :
We have,
BC = r_1 = radius of semicircular ARC
= 14/2
= 7 cm
AC = r_2 = radius of semicircular APB
= 7/2 cm
Now,
Perimeter of shaded region
= Perimeter of (arc APB + arc BSD + arc APB + arc QCD
= perimeter of (2 arc ARP + 2 arc ACB)
(arc ARC = arc BSD , arc CQD = arc APB)
= 2 x ½ x 2πr_1 + 2 x ½ x 2πr_2
= 2πr_1 + 2πr_2
= 2π(r_1 + r_2)
= 2πr x 7 + 7/2 cm
= 2π. 21/2
= 21π cm
= 21 x 21/7
= 66 cm
∴ Perimeter of shaded region is 66cm
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