Question

Find the area of the shaded portion in the following figure.

Answer 1

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