Thomas' Calculus 13th Edition

$s=\frac{\sqrt 2}{2}d$ $a=\frac{1}{2}d^2$ $s$ - side $d$ - diagonal $a$ - area
We'll use s for side, d for diagonal and a for area. We know $s^2+s^2=d^2$, which makes $s^2=\frac{d^2}{2}$ Since $s^2=\frac{d^2}{2}$ and $s^2=a$, we can conclude that $a=\frac{d^2}{2}$