https://file.aiquickdraw.com/mathbot/file/1727139843771wenoi5p6.jpg

Let's break down the problem based on the floor plan you've provided and solve each part step by step.

### a. Find the lengths of all of the walls in the basement.

Looking at the image, the wall lengths are given directly or can be inferred from other dimensions:

- Top horizontal wall: 16 ft
- Top-right horizontal wall: 10 ft
- Vertical wall on the far right: 20 ft
- Bottom-right horizontal wall: 5 ft
- Bottom-left vertical wall: 12 ft
- Additional horizontal wall to the left of the 5 ft section: 4 ft
- Vertical wall next to the 4 ft section: 5 ft
- Remaining left horizontal wall at the top left: 16 ft

### b. What is the area of your basement floor?

The shape is complex, but we can break it down into rectangles:
1. Left rectangle: $ 16 \, \text{ft} \times 12 \, \text{ft} $
2. Right rectangle: $ 10 \, \text{ft} \times 20 \, \text{ft} $

We will subtract the small rectangle at the center (5 ft × 4 ft) since it is missing from the floor area.

### c. Carpet cost calculation

You are given a cost of $55/ft². Once we calculate the area of the basement, we multiply that by 55 to get the total carpet cost.

### d. Baseboard trim cost

Baseboard trim is applied along the perimeter of the walls. After summing up the total length of all the walls, we multiply that length by $3/ft to calculate the trim cost.

I'll now calculate the area and total costs for parts (b), (c), and (d).Here are the results for each part of the problem:

### a. Lengths of all the walls:
- Top horizontal wall: 16 ft
- Top-right horizontal wall: 10 ft
- Right vertical wall: 20 ft
- Bottom-right horizontal wall: 5 ft
- Bottom-left vertical wall: 12 ft
- Center horizontal wall: 4 ft
- Center vertical wall: 5 ft
- Left horizontal wall: 16 ft

Total wall length = **88 ft**

### b. Area of the basement floor:
Total area = **372 ft²**

### c. Carpet cost calculation:
Total carpet cost = **$20,460**

### d. Baseboard trim cost calculation:
Total trim cost = **$264**

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Do you want more details or have any questions about these calculations?

Here are 5 related questions:
1. How would the carpet cost change if the price per square foot increased by 10%?
2. If the dimensions of the missing rectangle were larger, how would that affect the total area and carpet cost?
3. How would the total perimeter change if one of the walls was extended by 2 feet?
4. What is the cost difference if the trim cost per foot increased from $3 to $4?
5. How would the total area change if the right rectangle had a width of 15 ft instead of 10 ft?

**Tip**: Breaking complex shapes into simple rectangles or other shapes often simplifies area and perimeter calculations.

The floor plan of the basement in your house is awkwardly shaped and shown below. Find the lengths of all of the walls, the area of the basement floor, the cost of carpeting, and the cost of trim.

Learn how to calculate the lengths of walls, area of a basement floor, and the costs for carpeting and trim using basic geometric principles. This problem involves breaking down an irregular shape into rectangles and using given unit costs. Suitable for students in Grades 7-9.

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