Assuming this is a square based pyramid you can use the Pythagorean Theorem. The hypotenuse is 10" and you have to find half the length of one of the diagonals of the base to get the second side. Finding half of the diagonal of the baseHalf the Hypotenuse of a isosceles triangle with sides 12" and 12") 12^2+12 ^2=C^2 C=16,97 Divide C/2 and you get one side of the bigger triangle within the pyramid, 8,49" Using that side and the slant length with the Pythagorean Theorem: 8,49^2+ H^2=10^2 H=5,29"