PQRS is a diameter of a circle of radius is 6 cm. the lenths PQ, QR and RS are equal. semicircles are drawn on PQ AND QS as shown in the above right side picture . find the perimeter and area of the shaded region ? NEED THIS ANS QUIKLY PLZZZZ
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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 6 2 + 3.14 x 2 2 - 3.14 x 4 2 ]
= 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 cm 2
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