Skip to main content
2 of 2
Image link broken; now fixed.
Joseph O'Rourke
  • 150.8k
  • 36
  • 358
  • 958

If I understand the question properly, the answer depends on the flexibility of the sheet. A fine cloth napkin might crease almost like origami, in which case the height would be half the diagonal of the square, $\sqrt{2}/2$ for a unit square:
Square fold
For more realistic physical models, the shape would be more bag-like, and the analysis more difficult.

Joseph O'Rourke
  • 150.8k
  • 36
  • 358
  • 958