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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 the right triangular prism, suppose that the sides of the triangular base measure 4 m, 5 m, and 6 m. The altitude is 7 m.

a) Find the lateral area of the prism.

b) Find the total area of the prism.

c) Find the volume of the prism.

Chapter 9.1, Problem 16E, For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 5 m, and

To determine

a)

To answer:

The lateral area of the prism.

In the accompanying right triangular prism, each base edge measures 4 m, 5 m, and 6 m.

The altitude is 7 m.

Elementary Geometry for College Students, Chapter 9.1, Problem 16E , additional homework tip  1

Explanation

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

The lateral area (L) of any solid prison with the perimeter of the base of the prism as (P) and altitude ‘h’ is given by the formula

L=Ph.

Here, P is the perimeter of any one of the base of the prism and which is given by the sum of all the sides of the base.

Calculation:

Given,

The measure of the base edges of the triangular prism =4 m, 5 m, and 6 m.

The altitude of the prism =7m.

The lateral area of any prism of altitude ‘h’ and of base perimeter P is given by

L=hP

Here, we have

h=7 m.

First, let us find the perimeter of the base of the prism

To determine

b)

To answer:

The total area of the prism.

In the accompanying right triangular prism, each base edge measures 4 m, 5 m, and 6 m.

The altitude is 7 m.

Elementary Geometry for College Students, Chapter 9.1, Problem 16E , additional homework tip  2

To determine

c)

To answer:

The volume of the prism.

In the accompanying right triangular prism, each base edge measures 4 m, 5 m, and 6 m.

The altitude is 7 m.

Elementary Geometry for College Students, Chapter 9.1, Problem 16E , additional homework tip  3

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