Δ ABC is an equilateral triangle.

Also, BC = AB = AC = 12 cm

The AD is the altitude at BC. Therefore, D is the midpoint of BC.

Now, ΔADB and ΔADC are right-angled triangles.

Applying Pythagoras theorem,

AB² = BD² + AD²

⇒ (12) ² = 6² + AD²

⇒ AD² = 144 – 36 = 108

⇒ AD = 6√3 cm