Australian AMC 2015 - Senior Question 21

Question 21

The diagram shows a regular hexagon with sides of length 1 inside a square. Four vertices of the hexagon lie on sides of the square; the other two vertices lie on a diagonal of the square.

What is the side length of the square?

Question illustration

$\sqrt3$
$6(\sqrt3-\sqrt2)$
$\frac12(\sqrt3+\sqrt2)$
$\frac12(\sqrt6+\sqrt2)$
2