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 Question from Britni, a student: The base of this pyramid is an equilateral triangle with sides 8 units. The altitude of the pyramid is square root of 3. What is its volume?

Britni,

We all know the nice formula for the area of a triangle, it is half the base times the height. If you know the length of the base then the location of the apex in not important, only its height above the base. All 4 triangles below have the same area.

A similar result is true for the volume of a pyramid. The volume of a pyramid is one third the area of the base times the height. Again if you know the area of the base then the location of the apex in not important, only its height above the base. Not even the shape of the base is important, only the area. In the diagram below if the pry amid with the square base, the tilted cone and the pyramid with the triangular base (a tetrahedron) have the same base areas then they have the same volumes.

Can you complete your problem now? If not then write back.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.