Problem 62

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Problem 62: (2007 AMC 10a, 18)

Consider the $12$-sided polygon $ABCDEFGHIJKL$, as shown. Each of its sides has length $4$, and each two consecutive sides form a right angle. Suppose that $\overline{AG}$ and $\overline{CH}$ meet at $M$. What is the area of quadrilateral $ABCM$?

$\text{(A)}\ \frac {44}{3}\qquad$ $ \text{(B)}\ 16 \qquad$ $ \text{(C)}\ \frac {88}{5}\qquad$ $ \text{(D)}\ 20 \qquad$ $ \text{(E)}\ \frac {62}{3}$

Solution

Exercise 62: Solution

The $12$-sided polygon $ABCDEFGHIJKL$ is shown. Each pair of consecutive sides is perpendicular. Every side has length $4$, except $BC$ and $FG$, which each have length $5$, and $DE$, which has length $2$. Segments $AG$ and $CH$ meet at $M$. What is the area of quadrilateral $ABCM$?

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