7.79cm It is an equilateral triangle so it has 3 equal sides. That means each side is 9cm.
Now draw a line from the top of the equilateral triangle to the base, and dividing it into two. You will have made two smaller triangles, with sides 9, 4.5, and h (the one you want to find).
A line drawn from the apex of an equilateral triangle to the midpoint of the base is perpendicular to the base, so you can use Pythagoras' Theorem!
4.5^2 + h^2 = 9^2
h = sqrt(9^2 - 4.5^2)
Therefore, the height is 7.79cm (2 decimal places)