Question

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the segment formed by the corresponding chord. (Use π = `22/7`)

Answer 1

Area of the segment APB = [Area of the sector AOB] − [Area of ΔAOB]             ....(1)

In AOB, OA = OB = 21 cm 

∴ ∠A =  ∠B =  60°          ...(∴ ∠O = 60°)

AOB is an equilateral triangle.

∴ AB = 21 cm

∴ Area of ΔAOB = `sqrt3/4` (side)²          ....[∴ ΔAOB is an equilateral triangle]

`= sqrt3/4 xx 21 xx 21  "cm"^2`

= `(441sqrt3)/4` cm²              ...(2)

Using part (ii) and (2) in (1), we have

Area of the segment = `[231  "cm"^2] − [(441sqrt3)/4  "cm"^2]`

`= (231 - (441sqrt3)/4)  "cm"^2`