Geometry: finding the area of a segement of a circle

[stuff123]

how do you find the area of a segement of a circle?

 

[tkhunny]

The WHOLE circle is \(\displaystyle \pi*r^{2}\). Part of the circle is proportional to the central angle.

 

[stapel]

Do you mean "segment", "sector", or something else?

What formulas have they given you?

What is the text of the exercise on which you're working?

Thank you.

Eliz.

 

[soroban]

Re: Geometry help

Hello, stuff123!

How do you find the area of a segement of a circle?

              * * *
          *:::::::::::*
        * - - - - - - - *
       *  \           /  *
            \       /r
      *       \ θ /       *
      *         *         *
      *                   *

       *                 *
        *               *
          *           *
              * * *

I assume we are given the radius \(\displaystyle r\) and the central angle \(\displaystyle \theta\) (in radians).

The area of the sector is found by this formula: \(\displaystyle \L\:A_s \:=\:\frac{1}{2}r^2\theta\)

The area of the triangle is: \(\displaystyle \L\:A_t\:=\:\frac{1}{2}r^2\sin\theta\)

Then the area of the segment is: \(\displaystyle \L\:A_s\,-\,A_t\)

 

[stuff123]

I think i know what to do now thanks alot if I have anymore questions I'll ask later.