Chapter 9.2, Problem 32E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

For its occupants to be protected from the elements, it was necessary that the teepee in Exercise 31 be enclosed. Find the amount of area to be covered; that is, determine the lateral area of the rectangular dodecagonal pyramid. Recall that its altitude measures

To determine

**To find:**

The lateral area of the pyramid.

Explanation

**Given:**

A teepee in shape of a regular pyramid with a dodecagon (12 sides) for the base as below,

and the height of the teepee is

**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.

The lateral area

The total surface area

According to the Pythagorean theorem, in a right-angled triangle

In a regular pyramid, the lengths of the apothem

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