Polya's "How to Solve It"

This problem was taken from the above mentioned book, which is considered a classic on concepts mathematical problem-solving skills. It is a good example of how algebra can be applied to geometry, and how the heuristic "working backwards" (and many others) can be applied to solve the problem.

Given all quadilaterals with the same perimeter, which one would have the biggest area?

Thanks to CJ for the correction.