Problem

2006 AMC 12B 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?

[asy] 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)); [/asy]

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AMC 12B
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