Circular sector

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A circular sector is shaded in green

A circular sector or circle sector, also known as a pie piece, is the portion of a circle enclosed by two radii and an arc. Its area can be calculated as described below.

Let θ be the central angle, in radians, and Failed to parse (Missing texvc executable; please see math/README to configure.): r

the radius. The total area of a circle is Failed to parse (Missing texvc executable; please see math/README to configure.): \pi r^2

. The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi

(because the area of the sector is proportional to the angle, and Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi
is the angle for the whole circle):

Failed to parse (Missing texvc executable; please see math/README to configure.): A = \pi r^2 \cdot \frac{\theta}{2 \pi} = r^2 \left( \frac{\theta}{2} \right) = \frac{1}{2} r^2 \theta.

Also, if Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

refers to the central angle in degrees, a similar formula can be derived.

Failed to parse (Missing texvc executable; please see math/README to configure.): A = \pi r^2 \cdot \frac{\theta}{360}

Sectors can have special relationships, which include halves, quadrants, and octants.

The perimeter of a sector is given by the following formula:

Failed to parse (Missing texvc executable; please see math/README to configure.): P = \left( \pi \cdot r \cdot \frac{\theta}{180}\right) + 2 \cdot r

where θ is in degrees.