



 
Hi Ariel, The expression \[\mbox{ the area of a sector of a circle of radius r } is \frac12 r^2 \theta.\] is valid if the angle is measured in radians. The diagram above is a circle of radius $r$ and a sector $S$ subtended by an angle of $\theta$ radians at the center of the circle. The area of the sector $S$ is a fraction of the area of the circle and the measure of the angle $\theta$ is a fraction of the measure of the angle subtending circle which is $2 \pi$ radians or $360^{o}.$ The symmetry of the circle implies that these two fractions are equal. That is \[\frac{\mbox{area of the sector S}}{\mbox{area of the circle}} = \frac{\theta}{2 \pi},\] or said slightly differently \[\mbox{area of the sector S} = \frac{\theta}{2 \pi} \times \mbox{area of the circle} = \frac{\theta}{2 \pi} \times \pi r^2 = \frac12 r^2 \theta.\] I hope this helps, 



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