   Chapter 9.4, Problem 4E 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

For a regular tetrahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler’s equation for that polyhedron.

To determine

To find:

The number of faces, vertices and edges in a regular tetrahedron and verify 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 tetrahedron is a regular polyhedron with four faces. All faces are congruent equilateral triangles.

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...

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