Twenty feet wire is used to make two figures? What is the maximum areas of enclosed figures.

Answer 1

max area for a given perimeter is a circle. Is the wire evenly divided?

If so, c = p/2, so r = p/4π, and the total area is

a = 2(πr^2) = 2π(p^2/16π^2) = p^2/8π

If not, then if we have a tiny circle, (area effectively zero), then r = p/2π and

a = πr^2 = πp^2/4π^2 = p^2/4π

I suspect there is something missing here from the problem statement.