Circle Sector and Segment
There are two main "slices" of a circle:
- The "pizza" slice is called a Sector.
- And the Segment, which is cut from the circle by a "chord" (a line between two points on the circle).
The Quadrant and Semicircle are two special types of Sector:
Half a circle is
Quarter of a circle is
Area of a Sector
You can work out the Area of a Sector by comparing its angle to the angle of a full circle.
Note: we are using radians for the angles.
This is the reasoning:
Area of Sector = θ2 × r2 (when θ is in radians)
Area of Sector = θ × π360 × r2 (when θ is in degrees)
Area of Segment
The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here).
There is a lengthy reason, but the result is a slight modification of the Sector formula:
Area of Segment = θ − sin(θ)2 × r2 (when θ is in radians)
Area of Segment = ( θ × π360 − sin(θ)2) × r2 (when θ is in degrees)
The arc length (of a Sector or Segment) is:
L = θ × r (when θ is in radians)
L = θ × π180 × r (when θ is in degrees)