The isoperimetric theorem states that of all convex 
-gons of a given perimeter, the
one which maximizes area is the regular 
-gon.
Isoperimetric Theorem
See also
Isoperimetric Inequality, Isoperimetric ProblemExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Isoperimetric Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IsoperimetricTheorem.html