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.

Arc with 3cm radius and 144 degree angle

Area of sector:

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

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

\[= 11.309...\]

\[= 11.31cm^{2}\]