   Chapter 8.CR, Problem 21CR 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

Find the area of a regular hexagon whose apothem has length 9 in.

To determine

To find:

The area of a regular hexagon.

Explanation

Formula:

If we are given the variables s and a, then we can solve for the area of the hexagon through the following formula:

A=12aP

In this equation, A is the area, P is the perimeter and a is the apothem.

We must calculate the perimeter using the side length and the equation

P=number of sides ×s

Where s is the side length.

Calculation:

The regular hexagon has apothem 9 in.

Let a = 9 in

The regular hexagon has six equal sides.

Sketch the following diagram:

To find side length (s):

Half of the length of one of the sides is part of a 30-60-90 triangle with the apothem. Thus:

a=x3x3=9x=93=93×33=933x=33

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