   Chapter 11.CT, Problem 20CT ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# Each apothem of regular pentagon ABCDE has length a. In terms of a, find an expression for the area A of pentagon ABCDE.__________

To determine

To find:

An expression to find the area of a regular pentagon ABCDE in terms of the apothem a.

Explanation

Given:

Each apothem of regular pentagon ABCDE has length a.

Theorem:

The area A of a regular polygon whose apothem has length a and whose perimeter is P is given by A=12aP.

In the diagram.

In the isosceles triangle OAF,

Let AB=2x m, OF=a.

In ∆AOF,  AOF= AOB2=722=36°

tan360=xa

x=a×tan360

x=0

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