The height of a regular triangular pyramid is 11, and the side edge of the pyramid is 14.

The height of a regular triangular pyramid is 11, and the side edge of the pyramid is 14. Find the side of the base of the pyramid.

In a right-angled triangle AOD, according to the Pythagorean theorem, we determine the length of the leg AO.

AO ^ 2 = AD ^ 2 – DO ^ 2 = 196 = 121 = 75.

AO = √75 = 5 * √3 cm.

In an equilateral triangle ABC, the heights are also its medians and at the point of their intersection are divided in the ratio 2/1, then OH = AO / 2 = 5 * √3 / 2, then AH = AO + OH = 5 * √3 + 5 * √3 / 2 = 15 * √3 / 2 cm.

AH is the height of an equilateral triangle which is: h = a * √3 / 2, where a is the side of the triangle, then a = BC = (15 * √3 / 2) * (2 / √3) = 15 cm.

Answer: The side of the base of the triangle is 15 cm.