   Chapter 9.4, Problem 6E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A regular polyhedron has 12 edges and 8 vertices.a) Use Euler’s equation to find the number of faces.b) Use the result from part (a) to name the regular polyhedron.

To determine

(a)

To find:

The number of faces using Euler’s equation.

Explanation

Approach:

A) Polyhedron

1) A polygon is a two dimensional shape form with more than two straight lines.

2) A polyhedron is a three-dimensional solid shape.

3) Each flat surface of a polyhedron is a polygon and is called a face.

4) The line segment where two faces of a polyhedron meet is called an edge.

5) The point where three or more edges of a polyhedron meet is called a vertex.

6) A regular polyhedron is a convex polyhedron whose faces are congruent regular polygons.

7) A regular hexahedron is a regular polyhedron with six congruent square faces.

B) Euler’s Equation

A very important relationship between the number of vertices, faces and edges of solid shapes was discovered by a Swiss mathematician Leonard Euler.

It states V+FE=2

To determine

(b)

To find:

The name of regular polyhedron.

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