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Question
Find the area of the shaded portion in a circle whose radius is 7 cm (see figure).
[Hint: Four right-angled triangles joined at right angles to form a square]
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Solution
Given that ABCD is a square
According to the question,
Area of square ABCD = 4 × Area of a right-angled triangle
∴ Area of square ABCD = 4 × Area of ΔAOB
= `4 xx (1/2 xx AO xx BO)` ...`[∵ "Area of a right angled triangle" = 1/2 xx "Base" xx "Height"]`
= 2 × 7 × 7
= 98 cm2 ...[∵ AO = BO = radius of circle = 7 cm, given]
Hence, the area of inscribed square is 98 cm2.
Area of shaded portion = Area of circle – Area of square
= πr2 – 98
= `22/7 xx 7 xx 7 - 98`
= 154 – 98
= 56 cm2
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