# ISEE Upper Level Math : How to find the length of an edge of a tetrahedron

## Example Questions

### Example Question #1 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 100 has four vertices with Cartesian coordinates where .

Evaluate       Explanation:

The tetrahedron is as follows (figure not to scale): This is a triangular pyramid with a right triangle with legs 10 and as its base; the area of the base is The height of the pyramid is 5, so Set this equal to 100 to get :  ### Example Question #2 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 1,000 has four vertices with Cartesian coordinates where .

Evaluate       Explanation:

The tetrahedron is as follows: This is a triangular pyramid with a right triangle with two legs of measure as its base; the area of the base is Since the height of the pyramid is also , the volume is .

Set this equal to 1,000:   ### Example Question #3 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 240 has four vertices with Cartesian coordinates where .

Evaluate       Explanation:

The tetrahedron is as follows (figure not to scale): This is a triangular pyramid with a right triangle with two legs of measure as its base; the area of the base is The height of the pyramid is 24, so the volume is Set this equal to 240 to get :    