11. (10 points) From a square plot of land, a rectangular plot 10 meters wide is marked out (as shown in the figure), leaving a rectangular plot with an area of 1575 square meters. What is the area of the rectangular plot that was marked out?



The above text is translated into English, preserving the original text's line breaks and format.
【Analysis】According to the problem, the difference between the length and width of the remaining rectangle is 10 meters. Since $1575=3 \times 3 \times 5 \times 5 \times 7=45 \times 35$, the side length of the original square is 45 meters. Therefore, the length and width of the cut-out rectangle are 45 meters and 10 meters, respectively. Based on this, the problem can be solved.

【Solution】According to the problem analysis, we have: $1575=3 \times 3 \times 5 \times 5 \times 7=45 \times 35$,
$$
45-35=10 \text {, }
$$

So the side length of the original square is 45 meters,
Then the area of the cut-out rectangle is: $45 \times 10=450$ (square meters),
Answer: The area of the cut-out rectangular land is 450 square meters.