The grid in the figure below is composed of 25 small unit squares. Determine:

a) How many squares with vertices on the points of the figure and sides on the segments of the figure exist?

b) How many pairs of parallel lines, each containing some segment of the figure, exist?

c) How many rectangles with vertices on the points of the figure and sides on the segments of the figure exist?

![](https://cdn.mathpix.com/cropped/2024_05_01_09dbad5281c800d666d6g-13.jpg?height=497&width=492&top_left_y=1800&top_left_x=862)
Solution

a) 55. Let's divide our count: