Question

in a circle of radius 21 cm an arc subtends an angle of 60° at the centre. Find area of the segment formed by corresponding chord of the arc.

Answer 1

Radius = 21 cm.

Angle subtend by the arc = 60° 

Area of the sector making angle 60° = (60°/360°) × π r2 cm2

                                          = (1/6) × 212π  = 441/6 π cm2
                               = 441/6 × 22/7 cm2 = 231 cm2
∴ Area of the sector formed by the arc is 231 cm2

Area of equilateral  ΔAOB = √3/4 × (OA)2 = √3/4 × 212 = (441√3)/4 cm2

Area of the segment formed by the corresponding chord 

                     = Area of the sector formed by the arc - Area of equilateral ΔAOB

                     = 231 cm2 - (441√3)/4 cm2