Chapter 9.2, Problem 28E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

For a regular square pyramid, the slant height of each lateral face has a measure equal to that of each edge of the base. If the lateral area is

To determine

**To find:**

The volume of the pyramid.

Explanation

**Given:**

A regular square pyramid with slant height of each lateral face 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 slant height of each lateral face equal to that of each edge of the base i.e.

The square base perimeter

The lateral area is

But it is given the lateral area is

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