Question

Find the area of the unshaded region shown in the given figure.

Answer 1

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