Let r be a radius of a given circle and α be an angle, that corresponds to a sector.
The circle area is [tex]A=\pi r^2[/tex] and denote the sector area as [tex]A_1[/tex].
Then [tex] \dfrac{A_1}{A}= \dfrac{\alpha}{2\pi} [/tex] (the ratio between area is the same as the ratio between coresponding angles).
[tex]A_1=\dfrac{\alpha}{2\pi} \cdot A=\dfrac{\alpha}{2\pi} \cdot \pi r^2= \dfrac{r^2\alpha}{2} [/tex].
