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 $ABCD$?

1. As shown in the problem, for a trapezoid with bases $AB$ and $CD$ whose diagonals meet at $K$, $[ABCD]=[AKD]\cdot\dfrac{(AB+CD)^2}{AB\cdot CD}$.
2. With $[AKD]=15$, $[ABCD]=15\cdot\dfrac{16^2}{60}=15\cdot\dfrac{256}{60}=64$.