   Chapter 8.CR, Problem 22CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

In a regular polygon, each central angle measures 45 ∘ .a) How many sides the regular polygon have?b) If each side measures 5 cm and the length of each apothem is approximately 6 cm, what is the approximate area of the polygon?

To determine

(a)

To find:

The number of sides the regular polygon have.

Explanation

Central angle:

A central angle of regular polygon is the angle formed by two consecutive radii of regular polygon.

Calculation:

It is stated that central angle of regular polygon is C=45

Suppose there are n sides in a regular polygon.

Then the measure of central angle of n side is

C=360n

Where n is the number of sides of polygon.

To find the regular polygon have how many sides we have to rearrange the above formula as follows:

To determine

(b)

To find:

The approximate area of the polygon.

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