Question

Find the area of the shaded portion in a circle whose radius is 7 cm (see figure).

[Hint: Four right-angled triangles joined at right angles to form a square]

Answer 1

Given that ABCD is a square

According to the question,

Area of square ABCD = 4 × Area of a right-angled triangle

∴ Area of square ABCD = 4 × Area of ΔAOB

= `4 xx (1/2 xx AO xx BO)`  ...`[∵ "Area of a right angled triangle" = 1/2 xx "Base" xx "Height"]`

= 2 × 7 × 7

= 98 cm²  ...[∵ AO = BO = radius of circle = 7 cm, given]

Hence, the area of inscribed square is 98 cm².

Area of shaded portion = Area of circle – Area of square

= πr² – 98

= `22/7 xx 7 xx 7 - 98`

= 154 – 98

= 56 cm²