Problem: The volume of a regular pyramid whose base is an equilateral triangle of side length and whose other edges are each of length , is
Answer Choices:
A.
B.
C.
D.
E. None of these
Solution:
The volume of any prramid is equal to one third the area of the bage times the ailitude. In the present problem, the area of the equilateral base of side is . The altitude is one leg of a right triangle with hypotenues an edge of the pyramid of length and the other leg the distance from the centroid to a vertex of the base of . Then . The required volume is
(Area of Base)(Altitude)