Enclosing Land by FencePieces

Source

I got this problem from Rustan Leino, who got it from Serdar Tasiran.

I solved it and wrote up my solution.

Problem    

You're given one 44-meter piece of fence and 48 one-meter pieces of fence. Assume each piece is a straight and unbendable. What's the largest area of (flat) land that you can enclose using these fence pieces?

Solution     Reveal