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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

In trapezoid ABCD,ABCD, AD‾\overline{AD} is perpendicular to DC‾,\overline{DC}, AD=AB=3,AD = AB = 3, and DC=6.DC = 6. In addition, EE is on DC‾,\overline{DC}, and BE‾\overline{BE} is parallel to AD‾.\overline{AD}. Find the area of △BEC.\triangle BEC.
33
4.54.5
66
99
1818
Answer: B
Concepts:triangle areatrapezoid
Small hint:
Figure out the base and height of triangle BECBEC.
Big hint:
Since ABEDABED is a square, DEDE and BEBE are both 3.3.
Solution:
We know that EC=DC−DE EC = DC - DE=6−3 = 6 - 3 =3.= 3. We also know that BE=AD=3. BE = AD = 3. Therefore, the area of △BEC\triangle BEC is 12⋅3⋅3=92. \dfrac{1}{2} \cdot 3 \cdot 3 = \dfrac{9}{2}.
Thus, B is the correct answer.
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