So given a perimeter of total length $L$ and $n$ edges that the shape must have what is the shape that maximizes the area?
The answer is probably a regular $n$-gon with lengths of $L/n$ but how do I prove it?
The motivation for the problem: I was thinking about how difficult it is to prove that the circle is the "best" in terms of area and why it's so difficult and this question naturally arises.
