Find the height of a right prism with base-rhombus.

Question

The base of a right prism is a rhombus. Find the height of the prism, if its diagonals are d1 and d2.

Answer 1

The hint.

Let $h$ be an altitude of the prism.

Thus, $$\left(\frac{\sqrt{d_1^2-h^2}}{2}\right)^2+\left(\frac{\sqrt{d_2^2-h^2}}{2}\right)^2=a^2.$$