Question

In figure, point O is the center of the circle.

∠AOB = 30º, OA = 12 cm.

Find the area of segment AXB (π = 3.14)

Answer 1

Given: Radius of the circle (r) = 12 cm

Central angle (θ) = 30°

π = 3.14

Formulae:

1. Area of sector = `(θ/360^circ) xx πr^2`

= `(30/360^circ) xx 3.14 xx (12)^2` 

= `1/12 xx 3.14 xx 144`

= 12 × 3.14

= 37.68 cm²

2. Area of triangle = `1/2 r^2 sinθ`

= `1/2 xx (12)^2 xx sin 30^circ`

= `1/2 xx 144 xx 1/2    ...[∵ sin 30^circ = 1/2]`

= `72 xx 1/2`

= 36 cm²

3. Area of segment = Area of sector − Area of triangle

Area of segment AXB = 37.68 − 36

= 1.68 cm²