To determine the cost of carpeting the family room, we first need to calculate the total area of the room and then convert that area into square yards. After that, we can calculate the cost of the carpeting.

Step 1: Divide the room into two rectangles

Based on the dimensions provided, the room consists of two connected rectangles:

• Rectangle 1 (Smaller rectangle):

  • Width (top edge) = 6 ft
  • Height (left edge) = 9 ft
  • Area of Rectangle 1 = $6 \, \text{ft} \times 9 \, \text{ft} = 54 \, \text{ft}^2$

• Rectangle 2 (Larger rectangle):

  • Width (top edge) = 11 ft
  • Height (right edge) = 11 ft
  • Area of Rectangle 2 = $11 \, \text{ft} \times 11 \, \text{ft} = 121 \, \text{ft}^2$

Step 2: Total area in square feet

The total area of the room is the sum of the areas of the two rectangles: $\text{Total area} = 54 \, \text{ft}^2 + 121 \, \text{ft}^2 = 175 \, \text{ft}^2$

Step 3: Convert square feet to square yards

Since $1 \, \text{yd}^2 = 9 \, \text{ft}^2$, we can convert the area into square yards by dividing by 9: $\text{Total area in square yards} = \frac{175 \, \text{ft}^2}{9} = 19.44 \, \text{yd}^2$

Step 4: Calculate the total cost

The cost of the carpet is $31 per square yard. Therefore, the total cost is: $\text{Total cost} = 19.44 \, \text{yd}^2 \times 31 \, \text{dollars/yd}^2 = 602.64 \, \text{dollars}$

Final Answer:

The total cost of carpeting the family room is $602.64.

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Would you like further details or have any questions? Here are some related questions to explore:

1. How would the cost change if the carpet price increased to $35 per square yard?
2. How does the total area change if the dimensions of the smaller rectangle are doubled?
3. What if the room had an irregular shape—how would you calculate the area then?
4. How would adding a small section of carpet waste (say, 10%) affect the total cost?
5. What happens to the cost if the room's dimensions are given in meters instead of feet?

Tip: Always ensure units are consistent throughout your calculations—this avoids errors when switching between square feet and square yards!