   Chapter 9.2, Problem 21E 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

In Exercises 20 and 21, use Theorem 9.2.1 in which the lengths of apothem a , altitude h , and slant height l of a regular pyramid are related by the equation l 2 = a 2 + h 2 .In a regular hexagonal pyramid whose base edges measure 2 3 i n . , the apothem of the base measures 3 i n . If the slant height of the pyramid is 5 i n . , find the length of its altitude.

To determine

To find:

The length of its altitude.

Explanation

Given:

A regular hexagonal pyramid whose base edges measure 23in., the apothem of the base measures 3in. and the slant height of the pyramid is 5in.

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 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 regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem; that is, l2=a2+h2.

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

Calculation:

Considering a regular hexagonal pyramid with vertex V and slant height l, height h, apothem a, lateral edge e, and radius r.

Given that base edges measure 23in

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