15. As shown in the figure, the area of square $\mathrm{ABCD}$ is 196 square centimeters, and it contains two partially overlapping smaller squares. The larger of the two smaller squares has an area that is 4 times the area of the smaller one, and the overlapping area of the two squares is 1 square centimeter. Therefore, the area of the shaded part is $\qquad$ square centimeters.
【Answer】 72
【Analysis】Key point: Skillful area calculation
The area of the square is 196, so the side length is 14. The overlapping area is 1, so the side length is 1; the area of the larger square is 4 times that of the smaller square, so the side length of the larger square is twice that of the smaller square, and the sum of the side lengths of the larger and smaller squares is $14+1=15$.
Therefore, the side length of the smaller square is $15 \div 3=5$, and the side length of the larger square is $5 \times 2=10$.
The area of the smaller rectangle is $(5-1) \times(10-1)=36$, so the area of the two smaller rectangles is $36 \times 2=72\left(\mathrm{~cm}^{2}\right)$.