2007 AMC 8 Problems/Problem 8

Problem

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

$\text{(A)}\ 3 \qquad \text{(B)}\ 4.5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 18$

Solution

We know that $ABED$ is a square with side length $3$ . We subtract $DC$ and $DE$ to get the length of $EC$ .

$EC = DC - DE = 6 - 3 = 3$

We are trying to find the area of $\triangle BEC$ .

So, $\frac{1}{2} * 3 * 3 = 4.5$ , $\boxed{B}$

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2007 AMC 8 Problems/Problem 8

Problem

Solution