   Chapter 9.1, Problem 13E 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

Generalize the results found in Exercise 11 and 12 by answering each of the following questions. Assume that the number of sides in each base of the prism is n. For the prism, what is thea) number of vertices?b) number of lateral edges?c) number of base edges?d) total of base of edges?e) number of lateral faces?f) number of bases?g) total number of faces?

To determine

a)

Assuming that the number of sides in each base of the prism is n, the number of vertices that the prism have, using the results found in Exercises 11 and 12.

Explanation

Calculation:

Given,

The number of sides in each base of the prism is n.

From Exercise 11(a)

For an octagonal prism,

The octagonal prism has 16 vertices.

(8 vertices at the upper base and 8 vertices at the lower base).

From Exercise 12 (a)

For a pentagonal prism,

The pentagonal prism has 10 vertices

To determine

b)

Assuming that the number of sides in each base of the prism is n, the number of lateral edges that the prism have, using the results found in Exercises 11 and 12.

To determine

c)

Assuming that the number of sides in each base of the prism is n, the number of base edges that the prism have, using the results found in Exercises 11 and 12.

To determine

d)

Assuming that the number of sides in each base of the prism is n, the total number of edges that the prism have, using the results found in Exercises 11 and 12.

To determine

e)

Assuming that the number of sides in each base of the prism is n, the number of lateral faces that the prism have, using the results found in Exercises 11 and 12.

To determine

f)

Assuming that the number of sides in each base of the prism is n, the number of bases that the prism have, using the results found in Exercises 11 and 12.

To determine

g)

Assuming that the number of sides in each base of the prism is n, the total number of faces that the prism have, using the results found in Exercises 11 and 12.

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