Area of a Circular Sector

Area of a Circular Sector

How to find the area of a circular sector: formula, example, and its solution.

Formula

A = pi*(r^2)*((theta)/360), A: area of a sector, pi: 3.141592..., r: radius of the arc, theta: measure of the arc's central arc (= measure of the arc)

A = πr2⋅(θ/360)

A: area of a sector
π: 3.141592...
r: radius of the arc
θ: measure of the arc's central angle
(= measure of the arc)

πr2: area of the circle
θ/360: ratio of (sector)/(circle)

This formula is quite similar to the length of an arc formula.

Example

Find the area of the given sector. r = 6. The measure of the central angle: 120.

r = 6, θ = 120

A = π⋅62⋅(120/360)