You want to install wall-to-wall carpeting in the family room. The floor plan is shown.

7 ft

10 ft

11 ft

11 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 7 ft.

The left edge of the smaller rectangle is 10 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 $33 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 your family room, we need to follow these steps:

### 1. Find the total area of the family room.
The floor plan consists of two rectangles. Let’s calculate the area of each rectangle separately, then add them together.

#### **Smaller rectangle:**
- Length = 10 ft (left edge of the smaller rectangle)
- Width = 7 ft (top edge of the smaller rectangle)

The area of the smaller rectangle is:
\[
\text{Area}_1 = 10 \, \text{ft} \times 7 \, \text{ft} = 70 \, \text{ft}^2
\]

#### **Larger rectangle:**
- Length = 11 ft (right edge of the larger rectangle)
- Width = 11 ft (top edge of the larger rectangle)

The area of the larger rectangle is:
\[
\text{Area}_2 = 11 \, \text{ft} \times 11 \, \text{ft} = 121 \, \text{ft}^2
\]

### 2. Add the areas together:
\[
\text{Total area} = \text{Area}_1 + \text{Area}_2 = 70 \, \text{ft}^2 + 121 \, \text{ft}^2 = 191 \, \text{ft}^2
\]

### 3. Convert square feet to square yards.
We know that:
\[
1 \, \text{yd}^2 = 9 \, \text{ft}^2
\]
So, the total area in square yards is:
\[
\text{Area in square yards} = \frac{191 \, \text{ft}^2}{9} = 21.22 \, \text{yd}^2
\]

### 4. Calculate the cost of carpeting.
The cost of the carpet is $33 per square yard. Therefore, the total cost is:
\[
\text{Cost} = 21.22 \, \text{yd}^2 \times 33 \, \frac{\text{dollars}}{\text{yd}^2} = 700.26 \, \text{dollars}
\]

### 5. Round the total cost to the nearest cent:
\[
\boxed{700.26}
\]

Thus, the total cost of carpeting your family room is **$700.26**.

Would you like further explanation or details on any step?

---

Here are 5 related questions you might find useful:
1. How do you calculate the area of composite shapes?
2. What is the process to convert square feet to square meters?
3. How do different carpet pricing models affect cost?
4. What other factors could influence carpeting costs (e.g., installation fees)?
5. How would the calculation change if you needed to account for waste or irregularities?

**Tip:** Always ensure that your units are consistent when calculating areas and costs—especially when converting between square feet and square yards!

You want to install wall-to-wall carpeting in the family room. The floor plan is shown.

7 ft

10 ft

11 ft

11 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 7 ft.

The left edge of the smaller rectangle is 10 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 $33 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.

Learn how to calculate the cost of installing carpet in a family room with a composite floor plan. This problem covers key geometric concepts, including calculating the area of rectangles, unit conversion from square feet to square yards, and pricing. Suitable for Grades 7-9.

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