# PSAT Math : Tetrahedrons

## Example Questions

### Example Question #252 : Psat Mathematics

Refer to the above tetrahedron, or four-faced solid. The surface area of the tetrahedron is 444. Evaluate  to the nearest tenth.

Explanation:

The tetrahedron has four faces, each of which is an equilateral triangle with sidelength . Since the total surface area is 444, each triangle has area one fourth of this, or 111. To find , set  in the formula for the area of an equilateral triangle:

### Example Question #253 : Psat Mathematics

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Insufficient information is given to answer the problem.

Explanation:

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

The height  of a pyramid can be calculated using the fomula

We set  and  and solve for :

### Example Question #254 : Psat Mathematics

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Explanation:

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

The volume of a pyramid can be calculated using the fomula

### Example Question #255 : Psat Mathematics

A regular tetrahedron has an edge length of . What is its volume?

Explanation:

The volume of a tetrahedron is found with the equation , where  represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

The volume of the tetrahedron is .

### Example Question #256 : Psat Mathematics

A regular tetrahedron has four congruent faces, each of which is an equilateral triangle.

A given tetrahedron has edges of length six inches. Give the total surface area of the tetrahedron.

Explanation:

The area of an equilateral triangle is given by the formula

Since there are four equilateral triangles that comprise the surface of the tetrahedron, the total surface area is

Substitute :

square inches.

### Example Question #257 : Psat Mathematics

Give the surface area of the above tetrahedron, or four-faced solid, to the nearest tenth.