Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 350: 35


The proof is below.

Work Step by Step

The figure below contains two triangles that are 45-45-90 triangles. Using this, we obtain that $s=\frac{d}{\sqrt2}$. Since the area of a square is $s^2$, we use substitution to find: $ A = (\frac{d}{\sqrt2})^2 = \frac{d^2}{2}$
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