PQRS is a diameter of a circle of radius 6cm The lengths PQ, QR and RS are equal - Maths - Areas Related to Circles

Question

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

Aparna S.p · Accepted Answer

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Solution : PS = 12 cm
As 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
= ½ [ 3 14 x 62 + 3 14 x
22 - 3 14 x 42]
= ½ [ 3 14 x 36 + 3 14 x 4 – 3 14 x 16 ]
= ½ [ 3 14 ( 36 + 4 – 16)]
= ½ ( 3 14 x 24 ) = ½ x 75 36
∴ Area of shaded region = 37 68 cm2

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.