Friday Puzzle

What is the area of the largest semicircle that can be inscribed in a unit square?

answer below (...and not as simple as might first appear):
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
answer:   π (3 − 2 √2) or ~ 0.539

(if you didn't get it, you can go here for the explanation:
http://www.qbyte.org/puzzles/p153s.html