AMC 12 2006b Problem 13

Rhombus $ABCD$ is similar to rhombus $BFDE$. The area of rhombus $ABCD$ is 24, and $\angle BAD = 60^\circ$. What is the area of rhombus $BFDE$?

defaultpen(linewidth(0.7)+fontsize(11));
unitsize(2cm);
pair A=origin, B=(2,0), C=(3, sqrt(3)), D=(1, sqrt(3)), E=(1, 1/sqrt(3)), F=(2, 2/sqrt(3));
pair point=(3/2, sqrt(3)/2);
draw(B--C--D--A--B--F--D--E--B);
label("$A$", A, dir(point--A));
label("$B$", B, dir(point--B));
label("$C$", C, dir(point--C));
label("$D$", D, dir(point--D));
label("$E$", E, dir(point--E));
label("$F$", F, dir(point--F));

$\textrm{(A) } 6 \textrm{(B) } 4\sqrt {3} \textrm{(C) } 8 \textrm{(D) } 9 \textrm{(E) } 6\sqrt {3}$