AMC8 2007

AMC8 2007 · Q8

AMC8 2007 · Q8. It mainly tests Triangles (properties), Area & perimeter.

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

梯形ABCD中，$\overline{AD}$ 与 $\overline{DC}$ 垂直，$AD = AB = 3$，$DC = 6$。此外，$E$ 在 $\overline{DC}$ 上，$BE$ 平行于 $\overline{AD}$。求 $\triangle BEC$ 的面积。

(A) 3 3

(B) 4.5 4.5

(D) 9 9

(E) 18 18

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) Note that $ABED$ is a square with side $3$. Subtract $DE$ from $DC$, to find that $EC$, the base of $\triangle BEC$, has length $3$. The area of $\triangle BEC$ is $\frac{1}{2}\cdot 3 \cdot 3=\frac{9}{2}=4.5$.

（B）注意到$ABED$是一个边长为$3$的正方形。用$DC$减去$DE$，可知$\overline{EC}$（$\triangle BEC$的底边）长度为$3$。$\triangle BEC$的面积为$\frac{1}{2}\cdot 3 \cdot 3=\frac{9}{2}=4.5$。

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