   Chapter 9.CR, Problem 7CR ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A regular square pyramid has a base whose sides are of length 10 cm each. The altitude of the pyramid measures 8cm. Find the length of the slant height.

To determine

To find:

The length of the slant height of the regular square 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 square pyramid has a base whose sides are of length 10 cm each. The altitude of the pyramid measures 8cm.

Calculation:

Let us consider regular square pyramid base of the figure,

The above figure shown that the apothem to any side has length 5 cm. (one-half the length of the side of the square base)

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. See the below figure.

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