2006 AMC 10B Problem 15 — Solution | LIVE by Po-Shen Loh

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2006 AMC 10B Problem 15

Attempt Problem 15 of the 2006 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10B solutions, or check the answer key.

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15.

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 $BFDE?$

$6$

$4\sqrt{3}$

$8$

$9$

$6\sqrt{3}$

Answer: C

Concepts:rhombus equilateral triangle congruence (geometry)

Difficulty rating: 1460

Solution:

Because $AB=AD$ and $\angle BAD=60^\circ,$ triangle $ABD$ is equilateral, and so is triangle $CBD.$

Points $E$ and $F$ split the rhombus into six congruent triangles, each of area $\tfrac{24}{6}=4.$

Rhombus $BFDE$ is the union of triangles $BED$ and $BFD,$ so its area is $2\cdot4=8.$

Thus, the correct answer is C.

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