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 #256 :Psat Mathematics

Aregular tetrahedronhas 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 #257 :Psat Mathematics

Tetra_1

Give the surface area of the abovetetrahedron, 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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