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

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:
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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.What Is a Sector?
A sector is a region of a circle bounded by two radii and the arc lying between the radii.
Why Does the Formula Work?
The area of a sector is just a fraction of the area of the circle of the same radius. The area is given by πr2, where r is the radius. For example, a sector that is half of a circle is half of the area of a circle.


Area of sector = θ⁄360° × πr2