A squared + B squared = C squared. C is the measurement from corner to corner. In this case C=38. Since we're dealing with a square, A = B.
Therefore, 2 * (A * A) = (38 * 38). or 2*(A*A) = 1444. If you divide 1444 by 2, you'll get the value for A*A.
A * A = 722. Now use the square root function on your calculator to get 26.87.
I would round up to 28 or 29 to allow for seam allowances and the fudge factor. As someone else said it's easier to trim fabric than add to it once it's cut.