Problem 263

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Problem 263: (2008 AMC 10a, 20)

Trapezoid $ABCD$ has bases $\overline{AB}$ and $\overline{CD}$ and diagonals intersecting at $K$. Suppose that $AB = 9$, $DC = 12$, and the area of $\triangle AKD$ is $24$. What is the area of trapezoid $ABCD$?

$\mathrm{(A)}\ 92\qquad$ $\mathrm{(B)}\ 94\qquad$ $\mathrm{(C)}\ 96\qquad$ $\mathrm{(D)}\ 98 \qquad$ $\mathrm{(E)}\ 100$

Solution

Exercise 263: Solution

Trapezoid $ABCD$ has bases $\overline{AB}$ and $\overline{CD}$ and diagonals intersecting at $K$. Suppose that $AB = 6$, $DC = 10$, and the area of $\triangle AKD$ is $15$. What is the area of trapezoid $ABCD$?

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