In a regular triangular pyramid SABC, the medians of the base ABC intersect at point O. The area of the triangle

In a regular triangular pyramid SABC, the medians of the base ABC intersect at point O. The area of the triangle ABC is equal to 2. The volume of the pyramid is 6. Find the length of the segment OS

Since the SABC pyramid is regular, its vertex point S is projected to point O, the point of intersection of the medians of the equilateral triangle ABC. Then the segment ОS is the height of the SABC pyramid.

Let’s apply the formula for the volume of the pyramid.

V = Sosn * h / 3.

h = 3 * V / Sb = 3 * 6/2 = 9 cm.

Answer: The length of the OS segment is 9 cm.