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 coolcat3 October 8th, 2013 11:08 AM

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.

 Pero October 8th, 2013 11:16 AM

Re: Help with finding an area of a sector

$\theta= \frac{s}{r}$

 coolcat3 October 8th, 2013 11:17 AM

Re: Help with finding an area of a sector

Thanks alot

 coolcat3 October 8th, 2013 11:22 AM

Re: Help with finding an area of a sector

Quote:
 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=?

 Pero October 8th, 2013 12:39 PM

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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