PSAT Math : How to find the surface area of a tetrahedron

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

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.

Possible Answers:

Correct answer:

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 #2 : How To Find The Surface Area Of A Tetrahedron

Tetra_1

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

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

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.

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