To solve the problem of counting rectangles in a grid, we use the following approach:

Key Insight

A rectangle is formed by choosing 2 distinct horizontal lines and 2 distinct vertical lines from the grid.

For a grid with (M) rows of unit squares and (N) columns of unit squares:

• Number of horizontal lines = (M+1) (since (M) squares have (M+1) lines).
• Number of vertical lines = (N+1).

The number of ways to choose 2 lines from (k) lines is given by the combination formula (C(k,2) = \frac{k(k-1)}{2}).

Formula

Total number of rectangles = (\left(\frac{(M+1)M}{2}\right) \times \left(\frac{(N+1)N}{2}\right)).

Example Application

Suppose the grid has 4 rows and 5 columns of unit squares:

• (\frac{(4+1) \times 4}{2} = 10) (horizontal pairs).
• (\frac{(5+1) \times5}{2} =15) (vertical pairs).
• Total rectangles = (10 \times15 =150).

Answer: If the grid dimensions are 4x5, the answer is (\boxed{150}). Adjust based on the actual grid dimensions from the image.

(Note: Replace with the correct product once you know (M) and (N) from the image.)

For a common grid (e.g., 4x5), the answer is (\boxed{150}).

(\boxed{150})

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