Geometry help please!

[catnipkitty]

With different shapes with the same perimeter, why does a circle Have the largest area? Simple explanation please, I've looked online and it's far too complicated!

I think its because the more sides you have in a shape the more area it has, so a square has less area than a hexagon of the same perimeter. A circle approximates an infinite number of sides thus it has the highest area.

Without calculus the way to show it is by attacking it from the other side, show that if you have a set of regular polygons and a circle of the same area then the circle has the smallest perimeter.