2022 AMC 10A Problem 5

Square ABCD has side length 1. Points P, Q, R, and S each lie on a side of ABCD such that APQCRS is an equilateral convex hexagon with side length s. What is s?

\textbf{(A) } \frac{\sqrt{2}}{3} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } 2 - \sqrt{2} \qquad \textbf{(D) } 1 - \frac{\sqrt{2}}{4} \qquad \textbf{(E) } \frac{2}{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.