# Sector

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$[asy]size(150); real angle1=30, angle2=120; pair O=origin, A=dir(angle2), B=dir(angle1); path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; fill(sector,gray(0.9)); D(unitcircle); D(A--O--B); MP("O",D(O),SSW); MP("A",D(A),NW); MP("B",D(B),NE); MP("\theta",(0.05,0.075),N);[/asy]$

A sector of a circle is a region bounded by two radii of the circle and an arc.

If the central angle of the sector is $\pi$ (or $180^{\circ}$), then the sector is a semicircle.

## Area

The area of a sector is found by multiplying the area of circle $O$ by $\frac{\theta}{2\pi}$, where $\theta$ is the central angle in radians.

Therefore, the area of a sector is $\frac{r^2\theta}{2}$, where $r$ is the radius and $\theta$ is the central angle in radians.

Alternatively, if $\theta$ is in degrees, the area is $\frac{\pi r^2\theta}{360^{\circ}}$.