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: <br /> ![Square fold][1] <br /> For more realistic physical models, the shape would be more bag-like, and the analysis more difficult. [1]: https://i.sstatic.net/MUv4V.jpg