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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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For Exercise 43 to 45, consider the oblique regular pentagonal prism shown. Each side of the base measures 12 cm, and the altitude measures 12 cm.

Find the volume of the prism.

Chapter 9.1, Problem 45E, For Exercise 43 to 45, consider the oblique regular pentagonal prism shown. Each side of the base

To determine

To find:

The volume of the prism.

Explanation

The volume of any solid is the region of space occupied by it and in general the volume of a solid is given by the product of its base area and altitude.

For a regular solid prism with base area B and altitude h, the volume is given by the formula

V=Bh.

Calculation:

Given,

The volume as a right prism with base area ‘B’ and altitude ‘h’ is given by

V=Bh

First let us calculate the base are of the prism.

The base of the prism is a regular polygon (pentagon) with apothem 8.2 cm and of side (edge) = 12 cm

The base area of a pentagon with perimeter ‘P’ and apothem ‘a’ is given by the formula

B=12aP

Here, the perimeter ‘P’ of the regular pentagonal prism is given by base edge with 5 since, a regular pentagonal prism has five edges of equal measure.

Thus,

P = Measure of an edge × 5

   =12×5

P = 60 cm

Now, substitute a = 8

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