  We will first solve the following problem analytically: given a piece of wire
of specified length, we will find where the wire should be cut and bent to form
two regular polygons not necessarily having the same number of sides, so that
the combined area of the polygons thus formed is maximized, minimized, greater
than, and less than a specified area. We will extend the results to the cases
where the wire is divided into three and finally into an arbitrary number of
segments. The second problem we will solve is as follows: two wires of
specified length are to be bent into two regular polygons whose total number of
sides is fixed. We will determine how the total number of polygonal sides are
to be allocated between the wires so that the total area of the polygons is
maximized. We will extend the results found here to the case where we are given
any number of wires of specified length.
