UNROLLING THESE CIRCLES GIVES…

 

…fills a triangle with base 2 π r and height r (where r is the radius of the filled disk). Such a triangle has area π r2. This does not serve as a complete proof for why this is the area of a circle, but can give you some intuition for why it should be.

Credit: matthen
http://blog.matthen.com/post/98459487701/unrolling-these-circles-fills-a-triangle-with-base