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:

area equals half time radius squared times angle

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:

angle, radius and 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?

sector with angle of 2 radians and a radius of 5 cm

Step-by-Step:

1

Start with the formula:

Area of sector = 12 r2θ

Don't forget: r2 = r × r (r squared).

2

Substitute the angle and the radius into the formula. In our example, θ = 2 and r = 5.

Area of sector = 12 × 52 × 2

Area of sector = 12 × 5 × 5 × 2

Area of sector = 25 cm2

Answer:

The area of a sector of a circle with a radius of 5 cm, with an angle of 2 radians, is 25 cm2.

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See Also

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