A floor plan of a kitchen and a living room are below.

Which expression can be used to determine the area of the kitchen?

Responses
A
12 n plus 20
B
9 n squared plus 30 n plus 16
C
15 n squared plus 13 n plus 2
D
9 n squared plus 48 n plus 64
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To determine which expression represents the area of the kitchen, we need to analyze the expressions given in the options. Unfortunately, without seeing the floor plan image directly, I can't analyze the dimensions of the kitchen and calculate the correct expression. However, I can guide you on how to approach the problem:

1. **Identify the Kitchen Area:** Look at the floor plan and identify the region labeled as the kitchen. Note its shape (rectangular, square, etc.) and its dimensions (length and width).

2. **Set Up the Expression:** If the dimensions are given in terms of a variable \(n\), you would need to use those dimensions to calculate the area. For example:
   - For a rectangular kitchen with dimensions \(a \times b\), where \(a\) and \(b\) might be expressions involving \(n\), the area would be \(a \times b\).

3. **Match the Area with the Choices:** The calculated expression for the area should match one of the given choices.

### Analysis of Options:
- **Option A:** \(12n + 20\) — A linear expression; represents perimeter, not area.
- **Option B:** \(9n^2 + 30n + 16\) — A quadratic expression; could represent an area.
- **Option C:** \(15n^2 + 13n + 2\) — A quadratic expression; could represent an area.
- **Option D:** \(9n^2 + 48n + 64\) — A quadratic expression; could represent an area.

Based on these options, you need to choose the one that correctly matches the dimensions of the kitchen on the floor plan.

If you provide the floor plan image or give specific dimensions, I can help you determine which option is correct.

Would you like more details on how to solve it with dimensions, or have any other questions? 

### Related Questions:
1. How do you calculate the area of different geometric shapes (e.g., rectangles, triangles)?
2. What are the characteristics of a quadratic expression in terms of representing area?
3. How can you convert a perimeter expression to an area expression?
4. What is the difference between linear, quadratic, and cubic expressions in algebra?
5. How can you solve for \(n\) in a quadratic equation?

### Tip:
Always check if an algebraic expression represents a length, area, or volume by analyzing the terms involved (linear, squared, or cubic).

Explore how to determine the area of a kitchen using algebraic equations. Analyze options A, B, C, and D to match the correct expression to the kitchen's dimensions on the floor plan. Learn about quadratic expressions and their application in area calculations. Suitable for Grades 7-9.

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