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 8 - Section 8.3 - Regular Polygons and Area - Exercises - Page 378: 41

Answer

$$A =36\sqrt3+108$$

Work Step by Step

The area of the three squares is equal to: $$ A =3A_{square} \\ = 3(6^2) \\ =108$$ The area of the equilateral triangle is: $$ A = \frac{a^2\sqrt3}{4} \\ A=\frac{6^2\sqrt3}{4} \\ A=9\sqrt3$$ The isosceles trianges, in this case, have the same area. Thus, the total area is: $$ A = 4\cdot 9\sqrt3 +108 \\ A =36\sqrt3+108$$
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