31. The following rectangle is formed by nine pieces of squares of different sizes. Suppose that each side of the square $\mathrm{E}$ is of length $7 \mathrm{~cm}$. Let the area of the rectangle be $x \mathrm{~cm}^{2}$. Find the value of $x$.
31. Ans: 1056.
Let us use $|X|$ to denote the length of one side of square $X$. Thus $|E|=7$. Let $|H|$ be $a$ and $|D|$ be $b$. Then $|F|$ is $a+7,|B|$ is $a+14,|I|$ is $2 a+7,|G|$ is $3 a+7,|C|$ is $3 a+b+7$, and $|A|$ is $3 a+2 b+7$. Hence we have
$$
\begin{array}{l}
(3 a+2 b+7)+(a+14)=(3 a+b+7)+(3 a+7)+(2 a+7) \\
(3 a+2 b+7)+(3 a+b+7)=(a+14)+(a+7)+(2 a+7) .
\end{array}
$$

Therefore $a=1$ and $b=4$. Hence the area of the rectangle is $32 \times 33=1056$.