In a regular triangular pyramid SABC, the medians of the base ABC meet at point O

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

The segment SO is the height of the pyramid h, which we determine from the formula

the volume of the pyramid V = 1/3 * S main. * h.

where: V is the volume of the pyramid;

S main. – the area of the base of the pyramid;

h is the height of the pyramid.

h = V / S main. * 1/3;

h = 3V / S main;

h = 3 * 6: 2;

h = 9.

Answer: the segment SO (height of the pyramid) is 9.