Find the height of an equilateral triangle with side 6√3.

First, let’s find the area of ​​this triangle.

According to the problem statement, this triangle is equilateral and its side length is 6√3.

Since each angle of an equilateral triangle is 60 °, applying the formula for the area of ​​a triangle along two sides and the angle between them, we find the area S of this triangle:

S = 6√3 * 6√3 * sin (60 °) / 2 = 6√3 * 6√3 * (√3 / 2) / 2 = 36 * 3 * √3 / 4 = 27√3.

Applying the formula for the area of ​​a triangle through the height h drawn to its side, we find h:

h = 2 * S / (6√3) = 2 * 27√3 / (6√3) = 54√3 / (6√3) = 9.

Answer: The height of this equilateral triangle is 9.