Suppose a sector of a circle with radius [tex]r[/tex] has a central angle of [tex]\theta[/tex]. Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of a central angle to the measure of a full rotation of the circle. A full rotation of a circle is [tex]2\pi[/tex] radians. This proportion can be written as [tex]\boxed{\frac{A}{\pi r^{2}}=\frac{\theta}{2\pi}}[/tex]. Multiply both sides by [tex]\pi r^2[/tex] and simplify to get [tex]\boxed{A=\frac{\theta}{2} r^{2}}[/tex], where [tex]\theta[/tex] is the central angle of the sector and r is the radius of the circle.
