Let a be the length of a side of the equilateral triangle. Then altitude =
More precisely, if you draw a perpendicular from one vertex to the opposite side, it divides the side into two equal parts. If the equilateral triangle has side length s, then you have two right triangles with hypotenuse length s and one leg of length s/2. Use the Pythagorean theorem to find the length of the other leg, the altitude.
In general, if you draw a perpendicular from one vertex to the opposite side, it divides the side into two equal parts. If the equilateral triangle has side length s, then you have two right triangles with hypotenuse length s and one leg of length s/2. Use the Pythagorean theorem to find the length of the other leg, the altitude.