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Question
Find the area of the shaded portion in the following figure.
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Solution
Area of the given figure = Area of two semi-circles + Area of two triangles + Area of a square
∴ Area of triangle = `sqrt(s(s - a)(s - b)(s - c))` ...[∵ a = 5 cm, b = 5 cm and c = 6 cm, given]
Where, `s = (a + b + c)/2`
= `(5 + 5 + 6)/2`
= `16/2`
= 8 cm
∴ Area of a triangle = `sqrt(8(8 - 5)(8 - 5)(8 - 6))`
= `sqrt(8 xx 3 xx 3 xx 2)`
= `sqrt(144)`
= 12 cm2
∴ Area of 2 triangles = 2 × 12 = 24 cm2
∴ Area of 2 semi-circle = Area of 1 circle
Area of a circle = πr2
= `22/7 xx 3 xx 3`
= `(9 xx 22)/7`
= `198/7`
= 28.28 cm2
∴ Area of a square = 6 × 6 = 36 cm2
Area of the given figure = (24 + 28.28 + 36) = 88.28 cm2
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