MathDB
Two Similar Rhombi

Source: AMC 12 2006B, Problem 13

February 17, 2006
geometryrhombusAMC

Problem Statement

Rhombus ABCD ABCD is similar to rhombus BFDE BFDE. The area of rhombus ABCD ABCD is 24, and \angle BAD \equal{} 60^\circ. What is the area of rhombus BFDE BFDE?
[asy] size(180); defaultpen(linewidth(0.7)+fontsize(11)); 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("AA", A, dir(point--A)); label("BB", B, dir(point--B)); label("CC", C, dir(point--C)); label("DD", D, dir(point--D)); label("EE", E, dir(point--E)); label("FF", F, dir(point--F));[/asy]
<spanclass=latexbold>(A)</span>6<spanclass=latexbold>(B)</span>43<spanclass=latexbold>(C)</span>8<spanclass=latexbold>(D)</span>9<spanclass=latexbold>(E)</span>63 <span class='latex-bold'>(A) </span> 6 \qquad <span class='latex-bold'>(B) </span> 4\sqrt {3} \qquad <span class='latex-bold'>(C) </span> 8 \qquad <span class='latex-bold'>(D) </span> 9 \qquad <span class='latex-bold'>(E) </span> 6\sqrt {3}