[Answer] 124
[Solution] The shape formed by the points marked by Teacher Li is a triangle. Since the side length of this triangle is an integer, there is one more point on this side:
Categorization and discussion
(1) The three points are in three adjacent rows, with the following shapes:
(2) The three points are not in three adjacent rows, with the following shapes:

The first type has 8 shapes (including upside down and left-right reversal)
The second type has 16 shapes (including upside down and left-right reversal)

In total, there are $36+12+24+16+12+8+16=124$ shapes.
9. A rectangle is composed of 5 rows and 3 columns of small squares, with each small square having a side length of $1 \mathrm{~cm}$. This rectangle has 24 vertices. Choose 3 of these vertices to form a triangle with an area of 2.5 square centimeters. The number of such triangles in the rectangle is $\qquad$