The altitude forms a right angle triangle with half the side
length and one side as the hypotenuse.
Using Pythagoras:
(½side)² + altitude² = side²
→ altitude² = side² - ¼side²
→ altitude² = ¾side²
→ altitude = (√3)/2 × side
→ altitude = (√3)/2 × 6 = 3√3 ≈ 5.2