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]r2θ

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]⋅62⋅[2π/3].

Reduce the numerator 62 to, 62/6, 6
and cancel the denominator factors 2 and 3.

6⋅2π = 12π

So 12π is the answer.