To solve this problem, we need to calculate the area of the path surrounding the garden. Here's how:

Step 1: Dimensions of the garden

The garden is a rectangle with dimensions:

• Length = $35 \, \text{ft}$
• Width = $23 \, \text{ft}$

Step 2: Dimensions of the garden including the path

The path is $3 \, \text{ft}$ wide and surrounds the garden. Adding this width to all sides:

• New length (including the path) = $35 + 2(3) = 41 \, \text{ft}$
• New width (including the path) = $23 + 2(3) = 29 \, \text{ft}$

Step 3: Total area including the path

The total area of the garden and path is: $\text{Total area} = \text{New length} \times \text{New width} = 41 \times 29 = 1189 \, \text{ft}^2$

Step 4: Area of the garden

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

Step 5: Area of the path

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

Final Answer:

The area of the path is 384 ft².

Would you like further clarification on this solution?

Follow-Up Questions:

1. How is the concept of area extended when the path is non-rectangular?
2. What happens to the path area if the garden has irregular dimensions?
3. How can this problem be solved using algebraic expressions for different path widths?
4. How would the solution change if the path only surrounded two sides of the garden?
5. What real-life scenarios use similar calculations (e.g., fencing or landscaping)?

Tip:

Always double-check units to ensure consistency in your calculations!