11. (6 points) As shown in the figure, in the shape formed by a larger and a smaller square, the area of the shaded part is 50 square centimeters. Then the area of the smaller square is $\qquad$ square centimeters.
【Analysis】According to the problem, the shaded part is a triangle, which can be regarded as having the side length of the small square as its base, and the height is also the side length of the small square. Therefore, the area is equal to half of the area of the small square, so the area of the small square is $50 \times 2=100$ square centimeters.

【Solution】According to the analysis: The area of the small square is $50 \times 2=100$ (square centimeters). Answer: The area of the small square is 100 square centimeters.

Therefore, the answer is: 100.
【Comment】The main basis for solving this problem is: The area of a triangle is half of the area of a parallelogram with the same base and height.