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Sector

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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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Categories: Stubs | Definition | Geometry

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