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.

Insufficient information is given to answer the question.     Explanation:

The tetrahedron has four faces, each of which is an equilateral triangle with sidelength 7. Each face has area The total surface area is four times this, or about .

Rounded, this is 84.9. 