# PSAT Math : How to find the volume of a tetrahedron

## Example Questions

### Example Question #74 : Solid Geometry Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .    Insufficient information is given to answer the problem. Explanation:

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:    The height of a pyramid can be calculated using the fomula We set and and solve for :  ### Example Question #81 : Solid Geometry Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.      Explanation:

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:    The volume of a pyramid can be calculated using the fomula  ### Example Question #1 : Tetrahedrons

A regular tetrahedron has an edge length of . What is its volume?      Explanation:

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:   The volume of the tetrahedron is .

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