Let's solve this step by step.

Step 1: Count the shaded squares

We can see from the image that there are 12 shaded squares.

Step 2: Calculate the total area of the shaded squares

Each of the shaded squares has an area of 9 cm². So, the total area of the shaded squares is:

$12 \text{ squares} \times 9 \text{ cm}^2/\text{square} = 108 \text{ cm}^2$

Step 3: Total area of the rectangle

From the image, it seems the rectangle has 6 columns and 5 rows of squares, making the total number of squares (shaded and unshaded) 30.

Now, if each square has an area of 9 cm², the total area of the rectangle is:

$30 \text{ squares} \times 9 \text{ cm}^2/\text{square} = 270 \text{ cm}^2$

Step 4: Calculate the area of the unshaded portion

The unshaded area is the total area of the rectangle minus the area of the shaded squares:

$270 \text{ cm}^2 - 108 \text{ cm}^2 = 162 \text{ cm}^2$

Thus, the unshaded area of the rectangle is 162 cm².

Would you like more details on any of the steps, or have any questions? Here are some related questions to consider:

1. How would the total area change if the shaded squares had different areas?
2. What is the perimeter of the entire rectangle if the side length of each small square is known?
3. How could we calculate the unshaded area if the arrangement of shaded squares was irregular?
4. How would the solution change if the shape was not rectangular?
5. How do you calculate the side length of each square based on its area?

Tip: When dealing with geometric figures, it's helpful to count or calculate both the individual areas and the total areas step by step.