Answer:

Let ABC be the equilateral triangle with AD as an altitude from A meeting BC at D.

D will be the midpoint of BC.

Applying Pythagoras theorem in right-angled triangle ABD,

????????² = ????????² + ????????²

????????² = 12² − 6²

????????² = 144 − 36

=>108

???????? = √108

=>6√3 ????????.

The height of the given triangle is 6√3 ????????.