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

## Example Questions

### Example Question #1 : How To Find The Diagonal Of A Tetrahedron

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 #1 : How To Find The Diagonal Of A Tetrahedron

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 #2 : How To Find The Diagonal Of A Tetrahedron

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 . 