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

A regular octahedron has eight congruent faces, each of which is an equilateral triangle. 

A 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 : How To Find The Surface Area Of A Polyhedron

A regular icosahedron has 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 area  square centimeters.

The area of an equilateral triangle is given by the formula

Set  and solve for 

 centimeters.

 

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