   Chapter 9.2, Problem 19E 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 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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