To solve this problem:

Step 1: Determine the total area of the yard

The yard is a rectangle measuring 37 ft by 68 ft. The total area of the yard is: $\text{Area of yard} = 37 \times 68 = 2516 \, \text{ft}^2$

Step 2: Subtract the inner rectangle area

The walk is 2 ft wide, so the inner rectangle (excluding the walk) has dimensions reduced by 4 ft in both length and width (2 ft on each side): $\text{Inner length} = 68 - 4 = 64 \, \text{ft}$ $\text{Inner width} = 37 - 4 = 33 \, \text{ft}$ The area of the inner rectangle is: $\text{Area of inner rectangle} = 64 \times 33 = 2112 \, \text{ft}^2$

Step 3: Calculate the area of the walk

The area of the walk is the difference between the area of the yard and the area of the inner rectangle: $\text{Area of walk} = 2516 - 2112 = 404 \, \text{ft}^2$

Final Answer:

The area of the walk is: $\boxed{404 \, \text{ft}^2}$

Would you like further clarification or a breakdown of the steps?

Here are 5 related questions:

1. How would the result change if the width of the walk increased to 3 ft?
2. How can this concept be applied to circular yards?
3. What is the perimeter of the inner rectangle after subtracting the walk?
4. How do we calculate the cost of paving the walk if the cost per square foot is provided?
5. How could this problem be represented geometrically using algebraic expressions?

Tip: Always double-check dimension reductions (like subtracting twice the width of the walk) when calculating inner areas.