   Chapter 9.4, Problem 3E 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 figure (b) of Exercise 1, 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 the polyhedron 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.

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.

Where, V=Number of vertices, F=number of faces, E=number of edges.

Calculation:

In the polyhedron EFGHIJK,

The number of vertices (V) =7(E, F, G, H, I, J, K)

Number of faces (F) =9(ΔEFJ,ΔKFG,ΔIEH,ΔJ

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