Here you will learn perimeter and area of sector of circle formula with examples.

Let’s begin –

## What is Sector of a Circle ?

The region bounded by two radii of a circle and the arc intercepted by them is called a sector of the circle.

A sector is measured by the angle which its arc subtends at the centre of the circle.

**Also Read** : Formula for Length of Arc of Circle with Examples

## Perimeter of a Sector Formula

Perimeter = 2r + \(\pi r \theta\over 180\)

## Area of a Sector Formula

Area = \(\theta\over 360\) \(\times\) \(\pi r^2\) = \(\pi r^2 \theta\over 360\)

When length of the arc (\(l\)) is given, then area of sector

Area = \(1\over 2\) \(lr\)

**Example** : A sector is cut from a circle of diameter 21 cm. If the angle of the sector is 150, find its area.

**Solution** : We have,

Diameter = 21 cm \(\implies\) radius = \(21\over 2\) cm

Angle of sector = 150

Area of the sector = \(\theta\over 360\) \(\times\) \(\pi r^2\) = \(150\over 360\) \(\times\) \(22\over 7\) \(\times\) \(({21\over 2})^2\)

= \(5\over 12\) \(\times\) \(22\over 7\) \(\times\) \(21\over 2\) \(\times\) \(21\over 2\) = \(5\times 11\times 21\over 4\times 2\) = 144.38 \(cm^2\)

Hence, the area of sector is 144.38 \(cm^2\)

**Example** : The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.

**Solution** : Let O be the centre with radius 5.6 cm, and let OAB be its sector(as shown in figure above) with perimeter 27.2 cm

Then, OA + OB + arc AB = 27.2 cm

\(\implies\) 5.6 + 5.6 + arc AB = 27.2 cm

\(\implies\) arc AB = 16 cm

Area of the sector OAB = \(1\over 2\) \(\times\) radius \(\times\) arc length

= \(1\over 2\) \(\times\) 5.6 \(\times\) 16 = 44.8 \(cm^2\)

Hence, the area of sector is 44.8 \(cm^2\)