To solve this problem, let's break it down step by step:

Step 1: Calculate the total area of the garden including the path

The garden is surrounded by a path that is 3 feet wide. This means the total dimensions (including the garden and the path) are increased by 6 feet (3 feet on each side).

• Original garden dimensions: $23 \, \text{ft} \times 35 \, \text{ft}$
• Dimensions including the path: $\text{New length} = 23 \, \text{ft} + 6 \, \text{ft} = 29 \, \text{ft}$ $\text{New width} = 35 \, \text{ft} + 6 \, \text{ft} = 41 \, \text{ft}$
• Total area (garden + path): $\text{Total area} = 29 \, \text{ft} \times 41 \, \text{ft} = 1189 \, \text{ft}^2$

Step 2: Calculate the area of the garden alone

The area of the garden (without the path) is: $\text{Garden area} = 23 \, \text{ft} \times 35 \, \text{ft} = 805 \, \text{ft}^2$

Step 3: Calculate the area of the path

The area of the path is the difference between the total area and the garden area: $\text{Path area} = \text{Total area} - \text{Garden area}$ $\text{Path area} = 1189 \, \text{ft}^2 - 805 \, \text{ft}^2 = 384 \, \text{ft}^2$

Final Answer:

The area of the path is 384 ft².

Would you like a detailed breakdown of these steps or have additional questions? Here are some related questions for practice:

1. What would the area of the path be if it were 5 feet wide instead of 3 feet?
2. How do the calculations change if the garden is circular instead of rectangular?
3. What is the total perimeter of the garden including the path?
4. If the path is made of tiles costing $2 per square foot, what is the total cost of the path?
5. How would the area of the path change if the garden's dimensions doubled?

Tip: Always double-check units when solving area problems, especially when combining dimensions with added borders.