Question 666372
All diagonals intersect at the center of a square.

Also, the diagonal bisects the angle of the square. 

If you were to draw a line from O to the midpoint of A and C (C is in the bottom left corner we have ourselves a 45,45,90 triangle.

Recall that the sides of a 45 45 triangle are  a,a,asqrt(2).

well our asqrt(2) = 3 in this case so  3/sqrt(2) = 3sqrt(2)/2 is the length of a.

3sqrt(2)/2 is half the distance of the side of a square, so s = 3sqrt(2)

s^2 = (3sqrt(2))^2 =  9 * 2 = 18.