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 circular sector, pi: 3.141592..., r: Radius of a sector, theta: Measure of a sector's central angle

A = πr2⋅(θ/360)

A: Area of a circular sector
π = 3.141592...
r: Radius of a circular sector
θ: Measure of a sector's central angle

πr2 is the area of the whole circle.

θ/360 is the ratio of
(Sector's central angle, θ)/(Circle's central angle, 360).

Example

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

r = 6
θ = 120

So A = π⋅62⋅(120/360).

π⋅62 = 36π
120/360 = 1/3

So A = 36π⋅(1/3).

36⋅(1/3) = 12

So A = 12π.