In the given figure, PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn on PQ and QS as diameters. If PS = 12 cm, find the perimeter and the area of the shaded region.
Mensuration
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Question

In the given figure, PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn on PQ and QS as diameters. If PS = 12 cm, find the perimeter and the area of the shaded region.

Mensuration

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KnowledgeBoat · Accepted Answer

Given, PS = 12 cm PQ = QR = RS = = 4 cm, QS = 8 cm. Perimeter of shaded region = Arc PTS + Arc PBQ + Arc QES Radius of semi-circle PTS = = 6 cm. Arc PTS = × 2π.radius = πr = 3.14 × 6 = 18.84 cm. Radius of semi-circle PBQ = = 2 cm. Arc PBQ = π.radius = 3.14 × 2 = 6.28 cm. Radius of semi-circle QES = = 4 cm. Arc QES = π.radius = 3.14 × 4 = 12.56 cm. Perimeter of shaded region = Arc PTS + Arc PBQ + Arc QES = 18.84 + 6.28 + 12.56 = 37.68 cm. Area of shaded region = Area of big semicircle + Area of small semicircle on PQ - Area of semicircle on QS Calculating area of big semicircle, Area of small semicircle on PQ = π.(radius)2 = × 3.14 × 2^2 = 3.14 × 2 = 6.28 cm2. Area of semicircle on QS = π.(radius)2 = × 3.14 × 42 = 3.14 × 8 = 25.12 cm2 Area of shaded region = 56.52 + 6.28 - 25.12 = 37.68 cm2. Hence, area of shaded region = 37.68 cm2 and perimeter = 37.68 cm.

Mathematics

In the given figure, PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn on PQ and QS as diameters. If PS = 12 cm, find the perimeter and the area of the shaded region.

Mensuration

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