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 ⇒ 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 X 1/2 π(2)² = 16 + 8π cm²

Answer 2

Let assume that radius of semicircle drawn = r cm

r + r + r + r = 8 cm

4r = 8cm

r = \(\frac 82 \) = 4 cm

Area of unshaded region = \(2\times \pi r^2 + (2r)^2\)

\(= 2\pi r^2 + 4r^2\)

\(= 2r^2 (\pi + 2)\)

\(= 2 \times(2)^2 (\pi + 2)\)

\(= 8(\pi + 2) \ cm^2\) 

\(= 8\pi + 16\ cm^2\)