   Chapter 8.3, Problem 34E 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

Given regular hexagon A B C D E F with each side of the length 6 and the diagonal A C ¯ , find the area of pentagon A C D E F . To determine

To find:

The area of pentagon ACDEF.

Explanation

Calculation:

Given,

and the length of each side is 6

Calculation:

Consider the right angle triangle BGC.

The triangle  BGC is the form of 306090. Therefore by the properties of 306090 the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 angle. The longer leg, which is across from the 60 angle, is equal to multiplying the shorter leg by the 3.

i.e., BC=2BG, GC=3 ·BG

since BC=6,

2BG=6

BG=3

and

GC=3 ·BG

GC=33

From the figure AC=AG+GC

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