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: O is centre, ∠AOB = 30°, OA = OB = 12 cm, π = 3.14.

Step-wise calculation:

1. Area of sector AOB:

Formula: `"Area"_"sector" = (θ/360^circ) xx πr^2`.

Compute: `"Area"_"sector" = (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 AOB:

Use: `"Area"_"triangle" = 1/2 r^2 sinθ`.

sin 30° = 0.5

So, `"Area"_"triangle"` = 0.5 × 12² × 0.5

= 0.5 × 144 × 0.5

= 36.00 cm²

3. Area of minor segment AXB:

`"Area"_"segment" = "Area"_"sector" - "Area"_"triangle"`.

Compute: 37.68 – 36.00 = 1.68 cm².

Area of segment AXB = 1.68 cm².