【Solution】Solution: According to the analysis, as shown in the figure,
the areas of parts $a$ and $b$ can be perfectly combined to form a square with a side length of: $10-2 \times 1=8$ cm, the area of the region passed by the small square $=10 \times 10-8 \times 8=36$ (square cm).

Therefore, the answer is: 36.
4. (8 points) The side length of the larger square $A B C D$ is 10 cm, and the side length of the smaller square is 1 cm; as shown in the figure, the smaller square slides from $A$ to $B$ along the side $A B$, then from $B$ along the diagonal $B D$ to $D$, and then from $D$ along the side $D C$ to $C$; the area covered by the smaller square is $\qquad$ square centimeters.