The perimeter of a sector is the total distance around the boundaries of the sector. A sector of a circle is the region bounded by two radii of a circle. The length of the two radii and the length of the minor arc is the perimeter of a sector. On this page, we will discuss the perimeter of a sector in detail.

## How to find the perimeter of a sector

A sector is an area bounded by two radii and an arc is part of a circumference of a circle. A sector is bounded by two radii and an arc at the circumference of a circle. Now to find the perimeter of a sector we have to sum the lengths of the two radii with the length of the minor arc. We know that the length of an arc is = θ/360 × 2πr, where theta (θ) is the angle subtended by the two radii, π = 22/7, and r = radius of the circle. Therefore the formula for finding the perimeter of a sector = 2r + θ/360 × 2πr. Let’s understand the perimeter of a sector better by working through some examples.

Example 1. Find the perimeter of a sector of a circle whose radius is 14cm and the angle of sector AOB is 90°. [Take π = 3.142]

Solution

The perimeter of a sector = 2r + θ/360 × 2πr, where θ = 90°, r = 14cm, and π = 3.142

= 2(14) + 90/360 × 2 × 3.142 × 14

= 28 + 1/4 × 87.976

= 28 + 21.994

= 49.994cm

∴ The perimeter of the sector is = 49.994cm.

Example 2. If the length of a minor arc is 50.2cm. find the perimeter of a sector if the radius of the circle is 20cm.

Solution

The perimeter of a sector = 2r + θ/360 × 2πr, r = 20cm, and the length of the arc θ/360 × 2πr = 50.2cm.

= 2(20cm) + 50.2cm

= 40cm + 50.2cm

= 90.2cm

∴ The perimeter of the sector is = 90.2cm