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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 9.2, Problem 19E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
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Elementary Geometry for College St...

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

Consider any regular pyramid. Indicate which line segment has the greater length:

a) Slant height or apothem of base?

b) Lateral edge or slant height?

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 apothem a of a regular polygon is a line segment that is perpendicular from the center to the midpoint of one of its sides.

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, apothem a of a regular polygon is a line segment that is perpendicular from the center to the midpoint of one of its sides i

To determine

(b)

To find:

The line segment that is greater in length.

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Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E
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