# Advanced Geometry : How to find the diagonal of a tetrahedron

## Example Questions

### Example Question #15 : Tetrahedrons

Given a regular tetrahedron with an edge of , what is the height (or diagonal)? The height is the line drawn from one vertex perpendicular to the opposite face.    None of the above.  Explanation:

The height of a regular tetrahedron can be derived from the formula where is the length of one edge.

Therefore, plugging in the side length of , .

### Example Question #16 : Tetrahedrons

Given a regular tetrahedron with an edge of , what is the height (or diagonal)? The height is the line drawn from one vertex perpendicular to the opposite face.     None of the above. Explanation:

The height of a regular tetrahedron can be derived from the formula where is the length of one edge.

Plugging in we can solve for . ### Example Question #17 : Tetrahedrons

Find the height of this regular tetrahedron:      Explanation:

The height of a regular tetrahedron can be found using the formula where s is the length of the sides.

In this case, the sides have length , so we are multiplying .

We can simplify this by multiplying the numbers inside the radical: , which simplifies to . 