Let's go step by step to find the unshaded area of the rectangle.

1. Shaded Squares:

   • Each shaded square has an area of $9 \, \text{cm}^2$.
   • From the image, let's count the number of shaded squares. There are 14 small shaded squares.

2. Total Area of Shaded Squares:

   • The total area of the shaded squares is: $14 \times 9 = 126 \, \text{cm}^2$

3. Dimensions of the Rectangle:

   • The rectangle consists of a grid of squares. By counting, we see that the rectangle is 5 squares high and 7 squares wide.
   • Since each square has an area of $9 \, \text{cm}^2$, the side length of each square is $\sqrt{9} = 3 \, \text{cm}$.
   • Therefore, the dimensions of the rectangle are: $\text{Width} = 7 \times 3 = 21 \, \text{cm}, \quad \text{Height} = 5 \times 3 = 15 \, \text{cm}$

4. Total Area of the Rectangle:

   • The total area of the rectangle is: $21 \times 15 = 315 \, \text{cm}^2$

5. Unshaded Area:

   • The unshaded area is the total area of the rectangle minus the area of the shaded squares: $315 - 126 = 189 \, \text{cm}^2$

Thus, the unshaded area of the rectangle is 189 cm².

Let me know if you need further clarification or more details!

Related Questions:

1. How do you find the area of a rectangle if the dimensions are not given directly?
2. What is the process to find the side length of a square from its area?
3. How would you solve this problem if the shape were not rectangular?
4. How do you count the total number of squares in irregularly shaded patterns like this?
5. What if the problem asked for the percentage of the rectangle that is shaded?

Tip: Whenever dealing with problems involving areas, it's always helpful to break them down into known shapes like squares or rectangles, and use their properties to simplify the calculations.