Area of a circle, sector and segment

The area of a circle with radius $r$ is $A = ext{π} r^2$. The area of a sector with central angle $heta$ (in degrees) is $A = \frac{ heta}{360} ext{π} r^2$. The area of a segment is the area of the sector minus the area of the triangle formed by the two radii and the chord.

Important properties

• The area of a circle increases with the square of the radius.

• A sector's area is proportional to its central angle.

• The area of a segment can be found by subtracting the area of the triangle from the area of the sector.

• For a central angle in radians, sector area is $A = \frac{1}{2} r^2 \theta$.