# Sector of a Circle Area and Perimeter – Formula and Examples

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.

## 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 $$cm^2$$