A piece of paper in the shape of rectangle $ABCD$ has a point E marked on side $DC$ and a point F marked on side AB. When this paper is folded along line EF, AF and EC intersect perpendicularly as shown in the figure.
Given that the area of the figure obtained after the folding operation is $\mathbf { 18 }$ square units less than the area before the folding operation, what is the length |AD| in units?\\
A) 3\\
B) 4\\
C) 6\\
D) 8\\
E) 9