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

## Example Questions

### Example Question #51 : Advanced Geometry

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.

Possible Answers:

None of the above.

Correct answer:

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.

Possible Answers:

None of the above.

Correct answer:

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 #3 : How To Find The Diagonal Of A Tetrahedron

Find the height of this regular tetrahedron:

Possible Answers:

Correct answer:

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 .