Math CentralQuandaries & Queries


Question from Chelsea, a student:

There is a triangular pyramid which is an equilateral on the base with all sides 16.5 and the height is 25. I have to find the volume. Please help!

Hi Chelsea,

There is an amazing theorem that says that the volume of a cone is $\frac13 \times \mbox{ (the area of the base) } \times \mbox{ (the height) }$. A say amazing because it doesn't matter what the shape of the base is, as long as you can find its area, and the height is the perpendicular distance from the apex to the plane containing the base. For example, below is the skeleton of a pyramid with an oval shaped base and the apex not above the center of the oval.


You know the height of your pyramid and the base is an equilateral triangle. Can you find the area of an equilateral triangle?


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