Elementary Geometry for College Students (7th Edition)

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

Chapter 7 - Review Exercises - Page 349: 33


P=40$\sqrt 3$

Work Step by Step

In a regular hexagon, the length of the radius of a circle inscribed within it is equal to an apothem. The apothem of a regular hexagon is the long leg of a 30 60 90 triangle with half of a side as the short leg. Therefore: .5s=$\frac{a}{\sqrt 3}$ s=$\frac{20\sqrt 3}{3}$ P=6s P=6($\frac{20\sqrt 3}{3}$) P=40$\sqrt 3$
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