Explain how the formula for getting the area of the circle was derived

Question

ganeshie8 · Answer

One way is to inscribe a regular polygon of $n$ sides and calculate the polygon area

As $n -> \infty$, the area of polygon equals the area of circle

geerky42 · Answer

https://www.youtube.com/watch?v=YokKp3pwVFc

anonymous · Answer

http://en.wikipedia.org/wiki/Area_of_a_disk /thread

freckles · Answer

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If I did this right
we at least know the area of the circle is between 2r^2 and 4r^2
and we know pi is between 2 and 4
I know this doesn't exactly derive the formula 
but it estimates it 
by the way I found that one length using Pythagorean theorem