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PQRS is a diameter of a …

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PQRS is a diameter of a circle of radius 6cm and length PQ, QR and RS are equal. Find the perimeter of the shaded portion and area ot the non shaded portion

Posted by Theerthapramod Theertha 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 1 month ago

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 cm²

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