Textbook Problem

For the regular pentagonal prism shown below, find the total number of

a) edges. ______	b) faces. _______

To determine

a)

To find:

The total number of edges for the regular pentagon prism.

Answer to Problem 1CT

Solution:

The total number of edges in the regular pentagon prism is 15.

Explanation of Solution

Given:

The regular pentagon prism is shown below.’

Calculation:

We see that the base of the regular pentagon prism is a regular pentagon.

We know that there are five edges in a regular pentagon.

Therefore one base of the regular pentagon prism has five edges.

Since there are two bases, there are 10 base edges.

Also, there are five lateral edges.

Thus the number of edges in the regular pentagon prism is $10+5=15$ edges.

Final statement:

Therefore the total number of edges in the regular pentagon prism is 15.

To determine

b)

To find:

The total number of faces for the regular pentagon prism.

Answer to Problem 1CT

Solution:

The total number of faces in the regular pentagon prism is 7.

Explanation of Solution

Given:

The regular pentagon prism is shown below.’

Calculation:

We see that there are two base faces and five lateral faces.

Hence the total number of faces is 7.

Final statement:

Therefore the total number of faces in the regular pentagon prism is 7.