Question

In the figure, PQRS is a square with side 10 cm. The sectors drawn with P and R as centres form the shaded figure. Find the area of the shaded figure. (Use π = 3.14)

Answer 1

 
Sides of square = 10 cm

Radius of quadrant SEQR = 10 cm

∴ Area = `1/4` πr²

= `1/4 xx 22/7 xx 10 xx 10`

= 78.57 cm²

Area of triangle SQR = `1/2 xx QR xx SR`

= `1/2 xx 10 xx 10`

= 50 cm²

Area of segment SEQ = Area of quadrant SEQR – Area of ΔSQR

= 78·57 – 50

= 28.57 cm²

Total area of shaded portion = 2 × 28.57 = 57.14 cm²

As a result, the shaded portion's area is 57.14 cm².