Sector
![[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]](http://latex.artofproblemsolving.com/7/c/9/7c9a7756f90fe421d7f60125f66669fa9200d25d.png)
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 (or
), then the sector is a semicircle.
Area
The area of a sector is found by multiplying the area of circle by
, where
is the central angle in radians.
Therefore, the area of a sector is , where
is the radius and
is the central angle in radians.
Alternatively, if is in degrees, the area is
.
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