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

In a regular triangular pyramid SABC, the medians of the base intersect at point O. The area of triangle ABC is 28, OS = 12. Find the volume of the pyramid.

Since the SABS pyramid is regular, the ABC triangle at its base is equilateral, and its medians AH, BK and CM are its bisectors, and point O is the center of the inscribed and circumscribed circle and the projection of the vertex S onto the base plane, then SO is the height of the SABS pyramid …

Then Vpir = Sbn * SO / 3 = 28 * 12/3 = 112 cm3.

Answer: The volume of the pyramid is 112 cm3.