The problem in the image can be solved as follows:

Problem Breakdown:

The diagram represents a square backyard split into two areas:

• Patio Area (unshaded white squares).
• Garden Area (shaded green squares).

Each square represents $\frac{1}{100}$ (or 0.01) of the total backyard area. The total area of the backyard is 1 square unit. We are tasked to find the equation that represents the difference between the size of the garden and the size of the patio area.

Step 1: Determine the sizes of the patio and garden areas

From the diagram:

• The garden area (shaded) consists of 35 squares. Thus, the garden's size is: $0.01 \times 35 = 0.355$
• The patio area (unshaded) consists of 65 squares. Thus, the patio's size is: $0.01 \times 65 = 0.645$

Step 2: Calculate the difference between the two areas

The difference between the sizes of the garden and patio areas is: $0.645 - 0.355 = 0.29$

Step 3: Identify the correct equation

From the options provided:

• $D. \, 0.645 - 0.355 = 0.29$ correctly represents the difference.

Final Answer:

Option D: $0.645 - 0.355 = 0.29$

Do you need further explanation or details? 😊
Here are some follow-up questions to expand your understanding:

1. How would the calculations change if each square represented $\frac{1}{50}$ instead of $\frac{1}{100}$?
2. What is the ratio of the garden area to the patio area?
3. How would the difference be represented as a fraction instead of a decimal?
4. If the backyard were twice as large (2 square units total), what would be the size of each area?
5. How can this problem help you understand subtraction of decimals?

Tip: Always double-check diagrams for the exact count of areas to ensure accurate calculations.