Let and . The area of triangle BCD is , and the area of ABDE is . Hence the area of the pentagon P is
However you know that the perimeter is 10, so . Substitute into the area equation to obtain
Simplify, and differentiate both sides with respect to x and find critical points.
The area of the pentagon is
and the perimeter is
Substituting this into the area equation above produces
We locate the critical value:
Now you can find