Answer:
6√3 cm is the exact answer.
If you want it as a decimal correct to the nearest hundredth it is:
10.39 cm.
Explanation:
The height can be found using Pythagoras Theorem
The height is the perpendicular line drawn form any point to the opposite side. This forms a right triangle with base 1/2*12 ( = 6 cm) and hypotenuse = 12 cm.
So 12^2 = h^2 + 6^2
h^2 = 144 - 36
h^2 = 108
h = √108
= √36√3
= 6√3 cm.