# How to Find the Area of a Sector of a Circle (Radians)

## Finding the Area of a Sector of a Circle (Radians)

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

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

## How to Find the Area of a Sector of a Circle (Radians)

Finding the area of a sector of a circle, when the angle is in radians, is easy.

### Question

What is the area of the sector with an angle of 2 radians 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 = 2 and r = 5.

Area of sector = ^{1}⁄_{2} × 5^{2} × 2

Area of sector = ^{1}⁄_{2} × 5 × 5 × 2

Area of sector = 25 cm^{2}

### Answer:

The area of a sector of a circle with a radius of 5 cm, with an angle of 2 radians, is 25 cm^{2}.