Question

ps is a diameter of a circle of radius 6 cm Q and r are points on the diameter that diameter that PQ ,QR and RS are equal . semicircle are drawn with PQ and QS as diameter , as shown in the adjoining figure . find the perimeter of the shaded region also find the area of the shaded region ​

Answer 1

Answer:

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Answer 2

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  

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