Sector
![[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]](http://latex.artofproblemsolving.com/3/0/3/303f796fa9c544e25a8eab2c1c9de9508c532b8f.png)
A sector of a circle is a region bounded by two radii of the circle,
and
, and the arc
.
Area
The area of a sector , where
is in radians, is found by multiplying the area of circle
by
.
Therefore, the area of a sector , where
is the radius and
is in radians, is
.
Alternatively, if is in degrees, the area is
.
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