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 <math>r</math> the radius. The total area of a circle is <math>\pi r^2</math>. The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and <math>2 \pi</math> (because the area of the sector is proportional to the angle, and <math>2 \pi</math> is the angle for the whole circle):

<math>A =

\pi r^2 \cdot \frac{\theta}{2 \pi} = r^2 \left( \frac{\theta}{2} \right) = \frac{1}{2} r^2 \theta </math>.

Also, if <math>\theta</math> refers to the central angle in degrees, a similar formula can be derived.

<math>A = \pi r^2 \cdot \frac{\theta}{360}</math>

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

The perimeter of a sector is given by the following formula -: <math>P = ( \pi \cdot r \cdot \frac{\theta}{180}) + 2 \cdot r</math> where theta is in degrees.

[edit] See also

Circular segment - the part of the sector which remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary.