In a cuboid with a square base, the diagonal of the cuboid is the hypotenuse of a right triangle formed by the height (h) of the cuboid, one side of the base, and the diagonal of the base.

Let's call the side length of the square base "s" and the height of the cuboid "h." The diagonal of the cuboid (d) is given as 9 cm, and the side length of the square base (s) is 4 cm.

We can use the Pythagorean theorem to find the height (h):

\(d^2 = s^2 + h^2\)

Substitute the given values:

\(9^2 = 4^2 + h^2\)

Simplify:

\(81 = 16 + h^2\)

Now, subtract 16 from both sides:

\(h^2 = 81 - 16\)

\(h^2 = 65\)

To find the height (h), take the square root of both sides:

\(h = \sqrt{65}\)

So, the height of the cuboid is \(\sqrt{65}\) cm.