Problem Solving

Square ABCD is the base of the cube while EFGH is the cube's top facet such that point E is above point A, point F is above point B, etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of the square ABCD is 2?

$$A.\ \frac{1}{\sqrt{2}}$$
$$B.\ 1$$
$$C.\ \sqrt{2}$$
$$D.\ \sqrt{3}$$
$$E.\ 2\sqrt{3}$$

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.