AMC 12 2006a Problem 6

The $8\times 18$ rectangle $ABCD$ is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is $y$?

unitsize(3mm);
defaultpen(fontsize(10pt)+linewidth(.8pt));
dotfactor=4;
draw((0,4)--(18,4)--(18,-4)--(0,-4)--cycle);
draw((6,4)--(6,0)--(12,0)--(12,-4));
label("$A$",(0,4),NW);
label("$B$",(18,4),NE);
label("$C$",(18,-4),SE);
label("$D$",(0,-4),SW);
label("$y$",(3,4),S);
label("$y$",(15,-4),N);
label("$18$",(9,4),N);
label("$18$",(9,-4),S);
label("$8$",(0,0),W);
label("$8$",(18,0),E);
dot((0,4));
dot((18,4));
dot((18,-4));
dot((0,-4));

$\mathrm{(A) \ } 6 \mathrm{(B) \ } 7 \mathrm{(C) \ } 8 \mathrm{(D) \ } 9 \mathrm{(E) \ } 10$