   Chapter 9.CR, Problem 8CR 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

A regular hexagonal pyramid has a base whose sides are of length 6 3 in. each. If the slant height is 12 in., find the length of the altitude of the pyramid.

To determine

To find:

The length of the height of the regular hexagonal pyramid.

Explanation

Formula used:

Pythagorean Theorem:

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.

l2=a2+h2

Given:

A regular hexagonal pyramid has a base whose sides are of length 63 in. each. If the slant height is 12 in.

Calculation:

Let us consider regular hexagonal pyramid base of the figure,

The above figure shown that the right triangle to any side has length 33 in. (one-half the length of the side of the regular hexagonal base)

The regular hexagonal has a triangle is an equilateral triangle.

An equilateral triangle is also equiangular that is all three internal angles are also congruent to each other and are each 60.

A side of the regular hexagonal has an apothem length a is,

a=33tan60=333=33a=9in.

Then the slant height is l=12 in.

Also, the slant height is the hypotenuse of a right triangle with legs equal to the lengths of the altitude of the pyramid and the apothem of the base

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