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

## Example Questions

### Example Question #71 : Solid Geometry

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.

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 #1 : 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?

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.