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Sector

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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-...

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}}.

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Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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