10. (6 points) As shown in the figure, the side length of each small square is 1. Therefore, the number of shaded rectangles with an area of 2 in the figure is .



Translating the text as requested, while retaining the original formatting and line breaks.
【Analysis】According to the problem, the side length of each small square is 1, so the area is 1. An area of 2 should be the area of two small squares. To find how many shaded rectangles with an area of 2 there are in the figure, we need to count the number of adjacent pairs of small squares in the numbers $2$, $0$, $1$, and $4$, and then add them up to get the answer.

【Solution】Solution: In “2”, there are 10 shaded rectangles with an area of 2,
In “0”, there are 12 shaded rectangles with an area of 2,
In “1”, there are 4 shaded rectangles with an area of 2,
In “4”, there are 8 shaded rectangles with an area of 2,
So, in total, there are $10+12+4+8=34$ (rectangles).
Therefore, the answer is: 34.