   Chapter 9.CR, Problem 12CR ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

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

# The base of a regular pyramid is an equilateral triangle each of whose sides measure 12 cm. The height of the pyramid is 8 cm. Find the exact and approximate a) Lateral area b) total area c) volume.

To determine

(a)

To find:

The lateral area of the regular equilateral triangle pyramid.

Explanation

Formula used:

Lateral area L of any prism whose slant height has measure l and whose base has perimeter p is given by the formula,

L=12pl

Given:

The base of a regular pyramid is an equilateral triangle each of whose sides measure 12 cm. The height of the pyramid is 8 cm.

Calculation:

Let L=12pl(1)

In this problem, we first find the perimeter of the regular equilateral triangle pyramid.

Regular equilateral triangle pyramid as shown in the above figure.

The perimeter of regular equilateral triangle pyramid is given by the formula,

p=3s(2)

Where s is the each sides of the base of a regular equilateral triangle pyramid

To determine

(b)

To find:

The total area of the regular equilateral triangle pyramid.

To determine

(c)

To find:

The volume of the regular equilateral triangle pyramid.

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