9. As shown in Figure 1, five congruent shaded small squares are embedded within a unit square, and they do not overlap. The midpoints of the sides of the central small square are exactly the vertices of the other four small squares. If the side length of the small squares is $\frac{a-\sqrt{2}}{b}(a, b \in \mathbf{Z}_{+})$, then the value of $a+b$ is ( ).
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
9. E.

Let the side length of the small square be $x$, considering the diagonal of the large square. Then
$$
\begin{array}{l}
2 \sqrt{2} x + x = \sqrt{2} \Rightarrow x = \frac{4 - \sqrt{2}}{7} \\
\Rightarrow a = 4, b = 7 \Rightarrow a + b = 11 .
\end{array}
$$