The cube shown in the figure illustrates the calculation of the volume of a pyramid. The opposite vertices of the cube are connected, and the lines of connection meet at the center . This divided the cube into six congruent pyramids.
The volume of any one the six pyramids such as equals one-sixth of the volume of the cube and, therefore, the volume of one pyramid equals the area of the base times one-third of .
Thus, in this special case of a right square pyramid whose altitude equals one-half the length of a side of the base, we see that the volume of the pyramid equals the area of the base times one-third the altitude. In other words, the volume of the pyramid equals one-third the volume of a prism of the same base and altitude.
Rule: The volume of the pyramid equals the area of the base times one-third the altitude, i.e. , being area of base.
Find the volume of a pyramid whose base is an equilateral triangle of side m and whose height is m.
Since the base of pyramid is an equilateral triangle of side m,
The area of the base square m
The volume of the pyramid cubic m.