area of a sector

There are 360 degrees in a circle and the area of a whole circle is  \(\pi*r^2\)

so

are of a sector is the fraction of the circle that you have.  

 i.e.      \(\frac{sector\; angle \; }{360}\)

multiplied by the are of the whole circle.

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which is

\(\text{Area of sector }=\frac{sector\;angle\;in\;degrees}{360}\times \pi r^2 \qquad units^2 \)