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Sector

Revision as of 19:37, 24 April 2008 by I like pie (talk | contribs) (Added section Area)
[asy]size(150); real angle1=30, angle2=100; 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),NNW); MP("B",D(B),NE); MP("\theta",(0.075,0.075),N);[/asy]

A sector of a circle $O$ is a region bounded by two radii of the circle, $OA$ and $OB$, and the arc $AB$.

Area

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

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

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

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