Answer
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}$
