Please help!
Hello, aaronrpoole!
MartFL gave you a powerful hint.
But the answer is even simpler.
Consider the zigzag line.
We want the hypotenuse $\displaystyle d$ of a 4-by-8 right triangle.Code:* |. 3| . | . 4 *---.-----* : d. | : . | 5: . |5 : . | : .| * - - - - * 4
Then the side of the square is: $\displaystyle \frac{d}{\sqrt{2}}$
Therefore, the area of the square is: $\displaystyle \frac{d^2}{2}$