9. Find the sum of the areas of all different rectangles that can be formed using 9 squares (not necessarily all), if the side of each square is $1 \mathrm{~cm}$.
9. Solution. Let $a$ and $b$ be the lengths of the sides of the rectangle. If $a=1$, then $b=\{1 ; 2 ; \ldots ; 9\}$. If $a=2$, then $b=\{2 ; 3 ; 4\}$. If $a=3$, then $b=3$. The sum of the areas of all rectangles is $(1+2+\ldots+9)+2 \cdot(2+3+4)+3 \cdot 3=72$ (sq. cm). (MvSh)