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Two Squares: Rotated Inside Each Other

GMAT-VVXXYU

Each square has side length 1. The squares have the same center and are rotated $45^{\circ}$ from each other. How long is each side of the regular octagon which is formed?

A

$\cfrac{1}{3}$

B

$\cfrac{1}{2}$

C

$\cfrac{1}{\sqrt{2}}$

D

$\cfrac{1}{2+\sqrt{2}}$

E

$\cfrac{\sqrt{2}}{2+\sqrt{2}}$