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

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 Polyhedron

一个regular octahedronhas eight congruent faces, each of which is an equilateral triangle.

一个given octahedron has edges of length five inches. Give the total surface area of the octahedron.

Possible Answers:

Correct answer:

Explanation:

The area of an equilateral triangle is given by the formula

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

Substitute:

square inches.

Example Question #2 :Other Polyhedrons

一个regular icosahedronhas twenty congruent faces, each of which is an equilateral triangle.

The total surface area of a given regular icosahedron is 400 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?

Possible Answers:

Correct answer:

Explanation:

The total surface area of the icosahedron is 400 square centimeters; since the icosahedron comprises twenty congruent faces, each has areasquare centimeters.

The area of an equilateral triangle is given by the formula

Setand solve for:

centimeters.

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