SEARCH HOME
Math CentralQuandaries & Queries

search

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.

sector

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

About Math Central
 

 


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina