2007 AMC 8 Problem 8

Attempt Problem 8 of the 2007 AMC 8 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 2007 AMC 8 solutions, or check the answer key.

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In trapezoid $ABCD,$ $\overline{AD}$ is perpendicular to $\overline{DC},$ $AD = AB = 3,$ and $DC = 6.$ In addition, $E$ is on $\overline{DC},$ and $\overline{BE}$ is parallel to $\overline{AD}.$ Find the area of $\triangle BEC.$

$3$

$4.5$

$6$

$9$

$18$

Answer: B

Concepts:triangle area trapezoid

Difficulty rating: 960

Solution:

We know that $EC = DC - DE$ $= 6 - 3$ $= 3.$ We also know that $BE = AD = 3.$ Therefore, the area of $\triangle BEC$ is $\dfrac{1}{2} \cdot 3 \cdot 3 = \dfrac{9}{2}.$

Thus, B is the correct answer.

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