# Area of a Sector (in Radian)

How to find the area of a sector whose central angle is in radian: formula, 1 example, and its solution.

## Formula

### Formula

A = [1/2]r^{2}θ

A: Area of the sector

r: Radius of the sector

θ: Central angle of the sector (in radian)

Use this formula

when the central angle θ is in radian.

When the central angle is in degree measure,

use this formula.

## Example

### Example

### Solution

r = 6

θ = 2π/3

So A = [1/2]⋅6^{2}⋅[2π/3].

Reduce the numerator 6^{2} to, 6^{2}/6, 6

and cancel the denominator factors 2 and 3.

6⋅2π = 12π

So 12π is the answer.