Math CentralQuandaries & Queries


Question from mustafa, a student:

In a sector of a circle, the arc length is equal to half the perimeter of a sector. Find the area of a sector in terms of r


Suppose the length of the arc is $a$ units and the measure of the angle is $\theta$ units. You can use degrees or radians, it's your choice.


Write $a$ in terms of $a$ and $r.$

The perimeter of the sector is $a + 2r.$ Since the length of the arc is half the perimeter you have a equation relating $r$ and $\theta.$ Solve for $\theta.$

What is the area of the sector?


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