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Question
Find the area of the unshaded region shown in the given figure.
Solution
The side of a square = Diameter of the semi-circle = a
Area of the unshaded region
= Area of a square of side ‘a’ + 4(Area of a semi-circle of diameter ‘a’)
The horizontal/vertical extent of the white region = 14 – 3 – 3 = 8 cm
Radius of the semi-circle + Side of a square + Radius of the semi-circle = 8 cm
2 (radius of the semi-circle) + Side of a square = 8 cm
2a = 8 cm
`\implies` a = 4 cm
Area of the unshaded region
= Area of a square of side 4 cm + 4 (Area of a semi-circle of diameter 4 cm)
= `(4)^2 + 4 xx 1/2 π(2)^2`
= (16 + 8π) cm2
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