Question

PQRS is a diameter of an circle of radius of 6cm. The lengths PQ,QR and RS are equal . Semicircle are drawn with PQ and QS as diameters as shown. In the given figure if PS=12cm
The perimeter of the shaded region is

Answer 1

Answer:

Step-by-step explanation:

ps = 12 cm

⇒pq = qr =rs

∴ pq =qr =rs = 1/3 x ps = 1/3 x 12 = 4 cm.

qs = 2 pq

qs = 2 x 4 = 8 cm

∴ area of shaded region = area of semicircle with ps as diameter + area of semicircle with pq as diameter – area of semicircle with qs as diameter

= 1/2 [ 3.14 x 6² + 3.14 x 2² - 3.14 x 4² ]

= 1/2 [ 3.14 x 36 + 3.14 x 4 – 3.14 x 16 ] 

= 1/2[ 3.14 ( 36 + 4 – 16)]

= 1/2 ( 3.14 x 24 ) = 1/2 x 75.36 

∴ area of shaded region = 37.68 cm²

Perimeter of shaded region=12*22/7 =264/7