Polygon by Area
Ed Southall had a nice problem: find the regular polygon given the area and the number of sides.
http://solvemymaths.com/2015/08/03/area-problem-21/
I made a gif because I wondered what students might notice.
http://mathhombre.tumblr.com/post/125764699614/polygon-by-area-ed-southall-had-a-nice-problem
Playing with it further, noticed a crazy result for A=6 units^2, N=29.