To determine the cost of carpeting the hallway, we need to calculate the total area of the square and rectangular sections and then multiply by the cost per square yard.

1. Area of the square section: The area of a square is calculated as: $\text{Area of the square} = \text{side}^2 = 7 \times 7 = 49 \text{ square yards}.$

2. Area of the rectangular section: The area of a rectangle is calculated as: $\text{Area of the rectangle} = \text{length} \times \text{width} = 14 \times 7 = 98 \text{ square yards}.$

3. Total area: The total area of the hallway is the sum of the areas of the square and rectangular sections: $\text{Total area} = 49 + 98 = 147 \text{ square yards}.$

4. Cost of carpeting: The cost to carpet the hallway is calculated by multiplying the total area by the cost per square yard: $\text{Total cost} = 147 \times 24 = 3528 \text{ dollars}.$

Thus, the total cost to carpet the hallway is $3,528.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the cost change if the price of carpeting were $30 per square yard?
2. What is the perimeter of the hallway if both sections are combined?
3. If the hallway had only one rectangular section, how would the total cost be affected?
4. How much would it cost to carpet just the square section of the hallway?
5. How would the cost change if the dimensions of the rectangle were doubled?

Tip: Always ensure that you have the correct units for dimensions and pricing when calculating areas and costs!