Chapter 9.2, Problem 18E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Consider any regular pyramid. Indicate which line segment has the greater length:

**a)** slant height or altitude?

**b)** lateral edge or radius of the base?

To determine

**(a)**

**To find:**

The line segment that is greater in length.

Explanation

**Given:**

A regular pyramid.

**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.

In a regular pyramid with slant height

The altitude/height

The slant height

In a right-angled triangle, the hypotenuse is the longest side.

**Calculation:**

Considering a regular pyramid with vertex

Since, the altitude/height

To determine

**(b)**

**To find:**

The line segment that is greater in length.

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