Chapter 9.1, Problem 44E

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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 total area of the prism.

To determine

**To find:**

The total area of the prism.

Explanation

The total area of any solid is the area of all the number of lateral sides that it have, including the area of the top and the bottom of solid.

Thus, the total area

Here, we have

**Calculation:**

Given,

The total are of the any prism with lateral area L and base area B is given by

First let us calculate the lateral area of the prism.

The lateral area of any prism of altitude â€˜

Here, we have

But, the perimeter â€˜

Thus,

P = Measure of an edge

P = 60 cm

Thus, the lateral area of the parallelogram is given by

Now, calculate the base area of the prism.

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

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