   Chapter 11.2, Problem 44E 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 regular pentagon ABCDE, each radius has length r. in terms of r, find an expression for the perimeter of ABCDE.

To determine

To find:

An expression for the perimeter of ABCDE if regular pentagon ABCDE, each radius has length r.

Explanation

Consider the following figure,

The perimeter of pentagon is P=5a

The radii of a regular pentagon is r. the apothem bisect the base that is

DC=DE+ECa=DE+DE2DE=aDE=a2 Since, DE = EC

The central angle of the regular pentagon measures 3605 or 72

An apothem bisects its angle so, the angle formed by the apothem 36

General formula for cosine ratio and sin ratio is given below,

From the given figure the value radius r is the hypotenuse value since it is opposite to right angle

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