An irregular hexagon with all sides of equal length is placed inside a square of side length $1$, as shown below (not to scale). What is the length of one of the hexagon sides?
(a) $\sqrt{2} - 1,\quad$ (b) $2 - \sqrt{2},\quad$ (c) $1,\quad$ (d) $\dfrac{\sqrt{2}}{2},\quad$ (e) $2 + \sqrt{2}$.