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Sector
From Latin: sector "a cutter"
Definition: The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.
Try this Drag one of the orange dots that define the endpoints of the blue arc. The sector of the circle is shown in yellow.
(If there is no image below, see support page.)
As you can see from the figure above, a sector is a pie-shaped part of a circle. It has two straight sides (the two radius lines), the curved edge defined by the arc, and touches the center of the circle.
Attributes
Radius The radius of the circle of which the sector is a part
Central Angle The angle subtended by the sector to the center of the circle. See Central Angle of an Arc for more.

Area - central angle in degrees

where:
C  is the central angle in degrees
R  is the radius of the circle of which the sector is part.
π  is Pi, approximately 3.142

What this formula is doing is taking the area of the whole circle, and then taking a fraction of that depending on the central angle of the sector. So for example, if the central angle was 90°, then the sector would have an area equal to one quarter of the whole circle.

Area - central angle in radians*

If the central angle is in radians, the formula for the area of the sector is
where:
C  is the central angle in radians
R  is the radius of the circle of which the sector is part.

* Radians are another way of measuring angles instead of degrees. One radian is approximately 57.3°
   For more on this see Radians definition.

Other circle topics

General

Angles in a circle

Arcs

(C) 2009 Copyright John Page