My Math Forum Help with finding an area of a sector

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 October 8th, 2013, 11:08 AM #1 Newbie   Joined: Oct 2013 Posts: 3 Thanks: 0 Help with finding an area of a sector Hello, I am struggling to find the area of a sector when given the arc length s and central angle (Theta). I have the forumlas for it but the formula does not account for arc length s so I assume there is some type of exchange for another value. Any help would be appreciated.
 October 8th, 2013, 11:16 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Help with finding an area of a sector $\theta= \frac{s}{r}$
 October 8th, 2013, 11:17 AM #3 Newbie   Joined: Oct 2013 Posts: 3 Thanks: 0 Re: Help with finding an area of a sector Thanks alot
October 8th, 2013, 11:22 AM   #4
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Re: Help with finding an area of a sector

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 Originally Posted by coolcat3 Hello, I am struggling to find the area of a sector when given the arc length s and central angle (Theta). I have the forumlas for it but the formula does not account for arc length s so I assume there is some type of exchange for another value. Any help would be appreciated.
Here is an example. s =.3456ft, Theta = 73.61, A=?

 October 8th, 2013, 12:39 PM #5 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Help with finding an area of a sector If you're working in degrees, rather than radians, then: $\theta= \frac{360s}{2\pi r}$ $r= \frac{360s}{2\pi \theta}$ Once you have r, you have the area of the circle: $A= \pi r^2$ And the area of the sector is: $A_s= \frac{\theta}{360}A \ = \ \frac{90s^2}{\pi \theta}$

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