{"status": "success", "data": {"description_md": "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 $BFDE$?<br><center><img class=\"problem-image\" alt='[asy] 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(\"$A$\", 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]' class=\"latexcenter\" height=\"402\" src=\"https://latex.artofproblemsolving.com/4/3/e/43e4a11b576cfc60bb546ede67ebb9668484c340.png\" width=\"668\"/></center>\n\n$\\textrm{(A) } 6 \\qquad \\textrm{(B) } 4\\sqrt {3} \\qquad \\textrm{(C) } 8 \\qquad \\textrm{(D) } 9 \\qquad \\textrm{(E) } 6\\sqrt {3}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Rhombus  <span class=\"katex--inline\">ABCD</span>  is similar to rhombus  <span class=\"katex--inline\">BFDE</span> . The area of rhombus  <span class=\"katex--inline\">ABCD</span>  is 24, and  <span class=\"katex--inline\">\\angle BAD = 60^\\circ</span> . What is the area of rhombus  <span class=\"katex--inline\">BFDE</span> ?<br/><center><img class=\"latexcenter\" alt=\"[asy] 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(&#34;$A$&#34;, A, dir(point--A)); label(&#34;$B$&#34;, B, dir(point--B)); label(&#34;$C$&#34;, C, dir(point--C)); label(&#34;$D$&#34;, D, dir(point--D)); label(&#34;$E$&#34;, E, dir(point--E)); label(&#34;$F$&#34;, F, dir(point--F)); [/asy]\" height=\"402\" src=\"https://latex.artofproblemsolving.com/4/3/e/43e4a11b576cfc60bb546ede67ebb9668484c340.png\" width=\"668\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textrm{(A) } 6 \\qquad \\textrm{(B) } 4\\sqrt {3} \\qquad \\textrm{(C) } 8 \\qquad \\textrm{(D) } 9 \\qquad \\textrm{(E) } 6\\sqrt {3}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2006 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12B_p14", "prev": "/problem/06_amc12B_p12"}}