Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 343: 14

Answer

r=6 a=3$\sqrt 3$

Work Step by Step

Two consecutive radii and a side of a regular hexagon form an equilateral triangle. Therefore the radius and side is congruent. r=s r=6 The apothem splits the equilateral triangle into two 30 60 90 triangles where the apothem is the long leg. Therefore the apothem is equal to half of the side multiplied by the square root of 3. a=.5s($\sqrt 3$) a=3$\sqrt 3$
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