9. (10 points) As shown in the figure, the perimeter of the larger square is 80 centimeters more than that of the smaller square, and the area of the shaded part is 880 square centimeters. Therefore, what is the area of the larger square in square centimeters?

保留源文本的换行和格式，翻译结果如下：

9. (10 points) As shown in the figure, the perimeter of the larger square is 80 centimeters more than that of the smaller square, and the area of the shaded part is 880 square centimeters. Therefore, what is the area of the larger square in square centimeters?
【Analysis】By deforming the original figure, the side length of the small square in the upper right corner can be found based on the difference in perimeters, which in turn allows us to find the side length of the large square. Finally, using the area formula, we can calculate the area of the large square.

【Solution】
$$
\begin{aligned}
& 80 \div 4 = 20 \text{ (cm)} \\
& (880 - 20 \times 20) \div 20 \div 2 \\
= & (880 - 400) \div 20 \div 2 \\
= & 480 \div 20 \div 2 \\
= & 12 \text{ (cm)} \\
& (12 + 20) \times (12 + 20) \\
= & 32 \times 32 \\
= & 1024 \text{ (square cm)}
\end{aligned}
$$

Answer: The area of the large square is 1024 square cm.