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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Assume that the number of sides in the base of a pyramid is n . Generalize the results found in earlier exercises by answering each of the following questions.

a) What is the number of vertices?

b) What is the number of lateral edges?

c) What is the number of base edges?

d) What is the total number of edges?

e) What is the number of lateral faces?

f) What is the total number of faces?

(Note: Lateral faces and base =faces.)

To determine

(a)

To generalize:

The result for the number of vertices.

Explanation

Given:

The number of sides in the base of a pyramid is n.

Properties Used:

A pyramid is made by connecting a base to an apex or vertex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles. The altitude/height of the pyramid is the line segment from the vertex perpendicular to the plane of the base.

To determine

(b)

To generalize:

The result for the number of lateral edges.

To determine

(c)

To generalize:

The result for the number of base edges.

To determine

(d)

To generalize:

The result for the total number of edges.

To determine

(e)

To generalize:

The result for the number of lateral faces.

To determine

(f)

To generalize:

The result for the total number of faces.

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