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 344: 31

Answer

$4(1+\sqrt{2})$

Work Step by Step

In order to do this problem, we first must find the additional lengths in each corner of the figure, and then we add the length of ST. We know the corners contain 45-45-90 triangles, so: $ l = 4 \times \frac{\sqrt2}{2} \\ l = 2 \sqrt{2}$ Since there are two sides like this, we find: $RU = 2(2\sqrt{2}) + 4 = $$4(1+\sqrt{2})$
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