# GMAT Math : Calculating the length of an edge of a tetrahedron

## Example Questions

### Example Question #1 : Calculating The Length Of An Edge Of A Tetrahedron

Suppose the volume of the tetrahedron is .  What is the edge of the tetrahedron?

Explanation:

Write the formula to solve for the edge of a tetrahedron.

Substitute the volume and solve.

### Example Question #2 : Calculating The Length Of An Edge Of A Tetrahedron

The height of one of the equilateral triangle faces on a tetrahedron is  .  What is the side length of the tetrahedron?

Explanation:

Because a tetrahedron has four congruent equilateral triangles as its faces, we know the three equal angles of each face, as with all equilateral triangles, are each  .  We are given the height of a face, which is the length of a line that bisects one of the    angles and forms a right triangle with the side length as its hypotenuse. This means the angle between the height and the side length is  ,  whose cosine is equal to the adjacent side, the height, over the hypotenuse, the side length. This gives us:

### Example Question #3 : Calculating The Length Of An Edge Of A Tetrahedron

The volume of a tetrahedron is . What is the edge of the tetrahedron?

Explanation:

Write the formula to solve for the edge of a tetrahedron.

Substitute the given volume to the equation and solve.

### Example Question #4 : Calculating The Length Of An Edge Of A Tetrahedron

Find the exact edge length of a tetrahedron if the volume is .

Explanation:

Write the tetrahedron formula to solve for the edge.

Substitute the volume and simplify.

### Example Question #5 : Calculating The Length Of An Edge Of A Tetrahedron

A certain tetrahedron has a surface area of  .  What is the length of an edge of the tetrahedron?