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MATH / Rhombus ABCD is similar to rhombus BFDE. The area of rhombus ABCD is 24, and ∠BAD=60^(∘). What is the area of rhombus BFDE? [asy] pair A,B,C,D,I,F; A=(0,0); B=(10,0); C=(15,8.7); D…

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problem

Rhombus ABCDABCD is similar to rhombus BFDEBFDE. The area of rhombus ABCDABCD is 24, and ∠BAD=60∘\angle BAD=60^\circ. What is the area of rhombus BFDEBFDE? [asy] pair A,B,C,D,I,F; A=(0,0); B=(10,0); C=(15,8.7); D=(5,8.7); I=(5,2.88); F=(10,5.82); draw(A--B--C--D--cycle,linewidth(0.7)); draw(D--I--B--F--cycle,linewidth(0.7)); label("AA",A,SW); label("BB",B,SE); label("CC",C,NE); label("DD",D,NW); label("EE",I,W); label("FF",F,E); [/asy]
Plain-text mathematical notation (without MathML)
Rhombus ABCD is similar to rhombus BFDE. The area of rhombus ABCD is 24, and ∠BAD=60^(∘). What is the area of rhombus BFDE?

[asy]
pair A,B,C,D,I,F;
A=(0,0);
B=(10,0);
C=(15,8.7);
D=(5,8.7);
I=(5,2.88);
F=(10,5.82);
draw(A--B--C--D--cycle,linewidth(0.7));
draw(D--I--B--F--cycle,linewidth(0.7));
label("A",A,SW);
label("B",B,SE);
label("C",C,NE);
label("D",D,NW);
label("E",I,W);
label("F",F,E);
[/asy]
Original LaTeX notation
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]
pair A,B,C,D,I,F;
A=(0,0);
B=(10,0);
C=(15,8.7);
D=(5,8.7);
I=(5,2.88);
F=(10,5.82);
draw(A--B--C--D--cycle,linewidth(0.7));
draw(D--I--B--F--cycle,linewidth(0.7));
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,NE);
label("$D$",D,NW);
label("$E$",I,W);
label("$F$",F,E);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
48c090d3-ab30-5829-837f-b78c52005640
task_key
geometry--test--48c090d3-ab30-5829-837f-b78c52005640
task_revision_id
1
config / split
geometry / test

Official source

initial import