Question

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 14 cm, find the area of the shaded region.

Answer 1

Given:

Radius of larger circle, (OA) R = 7 cm

Diameter of small circle, (OD) = 7 cm

Radius of small circle = 7/2 cm

Height of ΔBCA (OC) = 7 cm

Base of ΔBCA (AB) = 14 cm

Area of ΔBCA = 1/2 × base × height

Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm²

Area of large semicircle with radius (OA) 7 cm = 1/2 × π × 7² = 1/2 × 22 × 7 × 7 × 7 = 77 cm²

Area of small circle with radius 7/2 cm = πr² = 22/7 × 7/2 × 7/2 = 77/2 cm²

Area of the shaded region = Area of small circle with radius 7/2 cm + Area of large semicircle with radius 7 cm - Area of ΔBCA

Area of the shaded region = 77/2 + 77 - 49 = 77/2 + 28 = (77 +56) / 2 = 133/2

Area of the shaded region = 66.5 cm²

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