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| Math Central | Quandaries & Queries |
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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 |
Hi,
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?
Penny
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