9. $(8,9)$ What is the maximum possible area of quadrilateral $A B C D$, the sides of which are $A B=1, B C=8, C D=7$ and $D A=4$?
Answer: 18.

Solution: Note that $1^{2}+8^{2}=7^{2}+4^{2}=65$. With fixed lengths of $A B$ and $B C$, the area of $\triangle A B C$ will be maximized if $\angle A B C=$ $90^{\circ}$. In this case, $A C=\sqrt{65}$, and thus $\angle B C D=$ $90^{\circ}$ as well, and the area of $\triangle B C D$ is also maximized.