   Chapter 9.2, Problem 18E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Consider any regular pyramid. Indicate which line segment has the greater length:a) slant height or altitude?b) lateral edge or radius of the base?

To determine

(a)

To find:

The line segment that is greater in length.

Explanation

Given:

A regular pyramid.

Properties Used:

A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

In a regular pyramid with slant height l, height h, apothem a, lateral edge e, and radius r,

The altitude/height h of the pyramid is the line segment from the vertex perpendicular to the plane of the base.

The slant height l of a regular pyramid is the altitude from the vertex (apex) of the pyramid to the base of any of the congruent lateral faces of the regular pyramid.

In a right-angled triangle, the hypotenuse is the longest side.

Calculation:

Considering a regular pyramid with vertex V and base a regular square ABCD, slant height l, height h, apothem a, lateral edge e, and radius r,

Since, the altitude/height h of the pyramid is the line segment from the vertex perpendicular to the plane of the base i

To determine

(b)

To find:

The line segment that is greater in length.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 