# Area of a Circluar Sector (in Radian)

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

## Formula

*A* = (1/2)*r*^{2}*θ**A*: area of a circular sector*r*: radius of the sector*θ*: radian measure of the arc's central angle

Area of a circular sector

## Proof

Recall the area of a circular sector (in degree):*A* = *πr*^{2}⋅[(degree)/360]

Change *π*⋅[(degree)/360]

to (1/2)⋅[*π*/180]⋅(degree).

[*π*/180]⋅(degree) = *θ* (radian)

Radian measure

## Example

*r* = 6, *θ* = 2*π*/3*A* = (1/2)⋅6^{2}⋅(2*π*/3)