You want to install wall-to-wall carpeting in the family room. The floor plan is shown.
6 ft9 ft11 ft11 ft
A floor plan consists of two rectangles. The right edge of the first, smaller rectangle is joined to the left edge of the second, larger rectangle. There are four measurements.
The top edge of the smaller rectangle is 6 ft.
The left edge of the smaller rectangle is 9 ft.
The top edge of the larger rectangle is 11 ft.
The right edge of the larger rectangle is 11 ft.
If the cost of the carpet you would like to purchase is $31 per square yard, what is the cost (in dollars) of carpeting your family room? Assume that there is no waste. Hint: 
9 ft2 = 1 yd2.
 (Round your answer to the nearest cent.)

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!

You want to install wall-to-wall carpeting in the family room. The floor plan is shown. A floor plan consists of two rectangles. The right edge of the first, smaller rectangle is joined to the left edge of the second, larger rectangle. There are four measurements: the top edge of the smaller rectangle is 6 ft, the left edge of the smaller rectangle is 9 ft, the top edge of the larger rectangle is 11 ft, and the right edge of the larger rectangle is 11 ft. If the cost of the carpet you would like to purchase is $31 per square yard, what is the cost (in dollars) of carpeting your family room? Assume that there is no waste. (Round your answer to the nearest cent.)

This problem teaches how to calculate the total cost of carpeting a room composed of two rectangles. Learn how to compute the area, convert square feet to square yards, and multiply by the carpet's cost per square yard. The solution explains step-by-step calculations, including the conversion of units and the final cost of carpeting. Ideal for students in Grades 6-8.

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