Since a [[Sector of a circle]] is a portion of a [[Circle|circle]] bounded, by two [[radius|radii]], the ratio of S, the area of the sector, to A, the [[area of a circle|area]] of the whole circle, is equal to the ratio of the [[Central angle of a Circle]] between its radii. In a sector with radius $r$ and central angle $\theta$ (radians), the area is $\pi r^2 \frac{\theta}{2\pi}=\frac12\theta r^2$ In a sector with radius $r$ and central angle $\theta\degree$, the area is $\pi r^2 \frac{\theta}{360}=\frac{\pi\theta r^2}{360}$ (a rigorous proof requires calculus) ![[area-of-arc.svg]]