Area of a sector is part of the area of a circle. A sector is any enclosed region bounded by two (radii) of a circle. A sector divides the circle into two, the minor sector and the major sector. On this page, we will discuss in detail how to find the area of a sector of a circle.

What is the area of a sector?

The area of a 2- dimensional figure is the measure of the amount of surface that an object can occupy. An area measured the size of the surface that an object can occupy. The area of a sector of a circle is the measure of the enclosed region bounded by two radii.

How to find the area of a sector

The area of an enclosed region is measured by finding the number of times the standard unit will fit into the space. The formula for finding the area of the sector POQ below is = θ/360° × area of a circle. i.e area of a sector = θ/360° × πr^{2}, where theta (θ) is the angle bounded by the two radii, π = 22/7 or 3.142, and r = radius of the circle.

Let’s understand the area of a sector of a circle better by working on some examples.

Example 1. If the area of a circle is 48cm^{2} . Find the area of the sector AOB of the circle given that ∠AOB is 60°.

Solution

The area of a sector of a circle = θ/360° × area of a circle

= 60°/360° × 48cm^{2}

= 1/6 × 48cm^{2}

= 8cm^{2}

∴ The area of a sector of the circle is 8cm^{2}

Example 2. Find the area of a sector of the circle POQ given that the angle POQ is 120° and the radius of the circle is 7cm.

Solution

The area of a sector = θ/360° × πr^{2} , where θ = 120°, π = 22/7 and r =7cm

= 120°/360° × 22/7 × 7^{2}

= 1/3 × 22 × 7

= 154/3

= 51.3cm^{2}