Question

Pqrs is a diameter of a circle of radius 6 cm take pi=22/7

Answer 1

If your question was: PQRS is a diameter of a circle of radius 6cm. The lengths PQ, QR and RS are equal. Semi circles are drawn on PQ and QS as diameters. Find the perimeter and area of the region so obtained,

Then,

Answer:

37.71 cm²

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 x 22/7

= 264/7 cm²

= 37.71 cm²