The square above is four feet high, four feet wide, and covers exactly half of the window's surface.

A number (actually a really large number) of people were confused by our solution. The reason being that we naturally associate the width and height of a square with the length of its edges. But because of this square's orientation, its height and width are the length of its diagonals.

Updated 3/15/1999:

Still to this day people write in pointing out that a square with four feet sides will cover more than the window. And they are correct. A square with four feet sides would never fit over the window. Of course, we never said the square's sides were four feet long, simply that the square is four feet high and four feet wide. The tinted blue square, while smaller than the window, is just as high and just as wide.