Chapter 9.2, Problem 27E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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For a regular square pyramid, suppose that the altitude has a measure equal to that of each edge of the base. If the volume of the pyramid is

To determine

**To find:**

The total area of the pyramid.

Explanation

**Given:**

A regular square pyramid as below,

and the altitude has a measure equal to that of each edge of the base i.e.

**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

The perimeter of the square is four times the side.

The volume

**Calculation:**

From the given figure

The sides of the square base measure

The area of the square base

Since, the volume

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