# 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? # 1

Start with the formula:

Area of sector = θ360° × πr2

Don't forget: π is pi (≈ 3.14), / means ÷ and r2 = r × r (r squared).

# 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 cm2

### Answer:

The area of a sector of a circle with a radius of 5 cm, with an angle of 72°, is 15.7 cm2.

## Slider

The slider below shows another real example of how to find the area of a sector of a circle.

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## See Also

What is a circle? What is an angle? What is pi? What are degrees? Finding the area of a circle What is a full angle?