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

2007 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

Page

Toolbox

Search

2007 AMC 8 Problems/Problem 8

Problem

Solution

See Also