Elementary Geometry for College Students (5th Edition)

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

Chapter 8 - Review Exercises: 25

Answer

$147\sqrt3$

Work Step by Step

The radius is the short side of a 30-60-90 triangle containing half of the base of the triangle and the apothem. Thus, we obtain: $ l = 7\sqrt{3}$ Since this is half of a side, we see that a whole side is $ s = 14\sqrt{3}$ We use the equation for the area of a equilateral triangle: $A = \frac{\sqrt3}{4}s^2 = \frac{\sqrt3}{4}(14\sqrt3)^2 = 147\sqrt3$
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