The height of an equilateral triangle is equal to the square root of three divided by two and multiplied by the length. The equation for the height of an equilateral triangle is based on the Pythagorean Theorem.
In an equilateral triangle, the height can be determined by creating two right triangles with an altitude drawn from one of the angles. The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the square of each side. Since each side is equal in length, the formula indicates that the length of a side squared equals the length of the hypotenuse squared plus the square of half the length.