Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 8 - Section 8.3 - Regular Polygons and Area - Exercises - Page 378: 26

Answer

1620 $ft^{2}$

Work Step by Step

Given in a regular dodecagon the approximate ratio of the length of an apothem to the length of a side is 15:8 For a regular dodecagon with a side of length 12 ft The area of a regular polygon whose apothem has length a and whose perimeter P is given by A = $\frac{1}{2}$ ap Lets take the ratio of apothem and side ratio 15:8. By proportionality constant x The apothem a = 15x side s= 8x But given side of length = 12 ft s = 8x = 12ft x = $\frac{12}{8}$ = 1.5 ft apothem of dodecagon a = 15x = 15* 1.5ft= 22.5 ft The perimeter of dodecagon P = 12s = 12 * 12 = 144 ft The area of octagon A = $\frac{1}{2}$ ap = $\frac{1}{2}$ *22.5 * 144 = 1620 $ft^{2}$
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