Question 5Square $ABCD$ 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?$$\dfrac{\sqrt{2}}{3}$$\dfrac{1}{2}$$2 - \sqrt{2}$$1 - \dfrac{\sqrt{2}}{4}$$\dfrac{2}{3}$