10. Let $\square A B C D$ be a trapezoid with parallel sides $A B$ and $C D$ of lengths 6 units and 8 units, respectively. Let $E$ be the point of intersection of the extensions of the nonparallel sides of the trapezoid. If the area of $\triangle B E A$ is 60 square units, what is the area of $\triangle B A D$ ?
Answer: 20
Solution: Note that $\triangle B E A \sim \triangle C E D$ and $|E B|=\frac{2 \cdot 60}{6}=20$. Thus, $|E C|=\frac{8}{6} \cdot 20=\frac{80}{3}$, and hence $|B C|=\frac{80}{3}-20=\frac{20}{3}$. Finally then,
area of $\triangle B A D=\frac{1}{2} \cdot 6 \cdot \frac{20}{3}=20$