Difference between revisions of "2006 AMC 12B Problems/Problem 13"

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(Problem)
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== Problem ==
 
== Problem ==
{{problem}}
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Rhombus <math> ABCD</math> is similar to rhombus <math> BFDE</math>.  The area of rhombus <math> ABCD</math> is 24, and <math> \angle BAD \equal{} 60^\circ</math>.  What is the area of rhombus <math> BFDE</math>?
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<asy> defaultpen(linewidth(0.7)+fontsize(11));
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pair A=origin, B=(2,0), C=(3, sqrt(3)), D=(1, sqrt(3)), E=(1, 1/sqrt(3)), F=(2, 2/sqrt(3));
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pair point=(3/2, sqrt(3)/2);
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draw(B--C--D--A--B--F--D--E--B);
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label("$A$", A, dir(point--A));
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label("$B$", B, dir(point--B));
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label("$C$", C, dir(point--C));
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label("$D$", D, dir(point--D));
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label("$E$", E, dir(point--E));
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label("$F$", F, dir(point--F));
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</asy>
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<math> \textrm{(A) } 6 \qquad \textrm{(B) } 4\sqrt {3} \qquad \textrm{(C) } 8 \qquad \textrm{(D) } 9 \qquad \textrm{(E) } 6\sqrt {3}</math>
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[[2006 AMC 12B Problems/Problem 13|Solution]]
  
 
== Solution ==
 
== Solution ==

Revision as of 19:08, 1 January 2012

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Problem

Rhombus $ABCD$ is similar to rhombus $BFDE$. The area of rhombus $ABCD$ is 24, and $\angle BAD \equal{} 60^\circ$ (Error compiling LaTeX. Unknown error_msg). What is the area of rhombus $BFDE$?

[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]

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

Solution

Solution

See also

2006 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions