Problem
2006 AMC 10B Problem 15
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?
![[asy] unitsize(3cm); defaultpen(.8); pair A=(0,0), B=(1,0), D=dir(60), C=B+D; draw(A--B--C--D--cycle); pair Ep = intersectionpoint( B -- (B+10*dir(150)), D -- (D+10*dir(270)) ); pair F = intersectionpoint( B -- (B+10*dir(90)), D -- (D+10*dir(330)) ); draw(B--Ep--D--F--cycle); label("$A$",A,SW); label("$B$",B,SE); label("$C$",C,NE); label("$D$",D,NW); label("$E$",Ep,SW); label("$F$",F,NE); [/asy]](/static/aops/c98fccf25fdaf81fa2ec0b3fdb8f1bae8255249c.png)
\mathrm{(A) \ } 6\qquad \mathrm{(B) \ } 4\sqrt{3}\qquad \mathrm{(C) \ } 8\qquad \mathrm{(D) \ } 9\qquad \mathrm{(E) \ } 6\sqrt{3}
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