9. (10 points) The figure is composed of 12 squares, each with an area of 1. How many rectangles in the figure have the same area as the shaded trapezoid?
Looking horizontally, the first three small squares in each row can form 1 rectangle with an area of 3, and the last three small squares can also form a rectangle with an area of 3, so there are 2 rectangles with an area of 3 in each row;
Horizontally, there are a total of: $3 \times 2=6$ (rectangles)
$$
4+6=10 \text { (rectangles) }
$$

Answer: There are 10 rectangles in the figure that have the same area as the shaded trapezoid.
Therefore, the answer is: 10.
[Comment] To solve this problem, first determine the side length of the squares to find the area of the shaded part, then find the number of rectangles with the same area.
【Analysis】Assuming the side length of the small square is 1, then the upper base of the trapezoid is 1, the lower base is 2, and the height is 2. According to the formula for the area of a trapezoid, the area of the shaded part is 3. The rectangle is formed by 3 small squares. Then, find out how many such rectangles there are when viewed horizontally and vertically, and add them together.

【Solution】Solution: Assuming the side length of the small square is 1, then the area of the trapezoid is:
$$
\begin{aligned}
& (1+2) \times 2 \div 2 \\
= & 3 \times 2 \div 2 \\
= & 3
\end{aligned}
$$

That is, the area of the rectangle is 3;
$1 \times 1=1$, the area of a small square is 1, so the rectangle is formed by 3 small squares,
Looking vertically, each column consists of 3 small squares, and there are 4 columns in total, so there are 4 rectangles that meet the requirements;