# Area of a sector

## Area of a sector

The area of a circle = $$\pi {r^2}$$.

The formula used to calculate the area of a sector of a circle is:

$Area\,of\,a\,sector = \frac{{Angle}}{{360^\circ }} \times \pi {r^2}$

## Example

### Question

Calculate the area of the sector shown in the diagram.

Area of sector:

$= \frac{{Angle}}{{360^\circ }} \times \pi {r^2}$

$= \frac{{144}}{{360}} \times \pi \times {3^2}$

$= 11.309...$

$= 11.31cm^{2}$