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Question
In the following figure, a rectangle ABCD enclosed three circles. If BC = 14 cm, find the area of the shaded portion (Take π = 22/7)
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Solution
AB = 14 + 14 + 14 + 7
= 49 cm
BC = 14 cm
AB = 49 cm
Area of ABCD = 49 × 14 cm2
Diameter of circle = 14 cm
Radius = `"Diameter"/2 = 7 cm`
Area of the circle = πr2
Area of the circle = `22/7xx7^2`
= `22/7xx49`
= `1078/7`
= 154 cm2
Area of 3 circles = 3 × 154 cm2
= 462 cm2
Area of the semicircle = `1/2` πr2
= `1/2xx22/7xx7^2`
= `22/14xx49`
= `1078/14`
= 77 cm2
⇒ Area of shaded portion = 686 – (462 + 77) cm2
= 686 – 539 cm2
= 147 cm2
Hence, the area of the shaded portion is 147 cm2.
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