# sector of a circle

A sector is a fraction of the interior of a circle, described by a central angle $\theta$. If $\theta=2\pi,$ the sector becomes a complete circle.

If the central angle is $\theta,$ and the radius of the circle is $r,$ then the area of the sector is given by

 $\frac{1}{2}r^{2}\theta$

This is obvious from the fact that the area of a sector is $\frac{\theta}{2\pi}$ times the area of the circle (which is $\pi r^{2}$). Note that, in the formula, $\theta$ is in radians.

Remark. Since the length $a$ of the arc of the sector is $r\theta$, the area of the sector is $\frac{1}{2}ar$, which is equal to the area of a triangle with base $=a$ and the height $=r$.

Title sector of a circle SectorOfACircle 2013-03-22 13:10:20 2013-03-22 13:10:20 CWoo (3771) CWoo (3771) 6 CWoo (3771) Definition msc 51-00 sector