# How to Find the Area of a Sector of a Circle

## Finding the Area of a Sector of a Circle

The area of a sector of a circle is given by the formula:

In this formula, **θ** is the angle (in degrees) of the sector and **r** is the radius of the circle. The image below shows what we mean by the area of a sector:

## How to Find the Area of a Sector of a Circle

Finding the area of a sector of a circle is easy.

### Question

What is the area of the sector with an angle of 72° and a radius of 5 cm, as shown below?

### Step-by-Step:

# 1

# 2

Substitute the angle and the radius into the formula. In our example, θ = 72° and r = 5.

Area of sector = ^{72°}⁄_{360°} × π × 5 × 5

Area of sector = (72° ÷ 360°) × 25 × π

Area of sector = 15.7 cm^{2}

### Answer:

The area of a sector of a circle with a radius of 5 cm, with an angle of 72°, is 15.7 cm^{2}.