Difference between revisions of "2006 AMC 12B Problems/Problem 13"
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== 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>? | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | [[2006 AMC 12B Problems/Problem 13|Solution]] | ||
== Solution == | == Solution == | ||
Revision as of 18:08, 1 January 2012
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Problem
Rhombus 
is similar to rhombus 
. The area of rhombus is 24, and $\angle BAD \equal{} 60^\circ$ (Error compiling LaTeX. Unknown error_msg). What is the area of rhombus ?
![[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]](http://latex.artofproblemsolving.com/4/3/e/43e4a11b576cfc60bb546ede67ebb9668484c340.png)
Solution
See also
| 2006 AMC 12B (Problems • Answer Key • Resources) | |
| 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 | |
