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:

area of sector equals angle divided by 360 all times pi times radius squared

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:

area, angle and radius

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?

area of sector with angle of 72 degrees and a radius of 5 cm

Step-by-Step:

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.

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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?