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To solve this problem, we are tasked with determining a simplified expression that represents the **total area** of Room 2 and Room 4.

### Given Information:

- **Room 2** is a rectangle with dimensions:
  - Length = \( x + 9 \)
  - Width = \( 3 \)

- **Room 4** is also a rectangle with dimensions:
  - Length = \( 4 \)
  - Width = \( x - 4 \)

### Step-by-Step Calculation:

1. **Area of Room 2**:
   The area of a rectangle is calculated by multiplying its length by its width. 
   \[
   \text{Area of Room 2} = (\text{Length of Room 2}) \times (\text{Width of Room 2})
   \]
   Substituting the given values:
   \[
   \text{Area of Room 2} = (x + 9) \times 3 = 3(x + 9)
   \]
   Simplifying:
   \[
   \text{Area of Room 2} = 3x + 27
   \]

2. **Area of Room 4**:
   Similarly, the area of Room 4 is:
   \[
   \text{Area of Room 4} = (\text{Length of Room 4}) \times (\text{Width of Room 4})
   \]
   Substituting the given values:
   \[
   \text{Area of Room 4} = 4 \times (x - 4) = 4(x - 4)
   \]
   Simplifying:
   \[
   \text{Area of Room 4} = 4x - 16
   \]

3. **Total Area of Room 2 and Room 4**:
   Now, we add the areas of Room 2 and Room 4:
   \[
   \text{Total Area} = (3x + 27) + (4x - 16)
   \]
   Combine like terms:
   \[
   \text{Total Area} = 3x + 4x + 27 - 16 = 7x + 11
   \]

### Final Answer:
The simplified expression representing the **total area of Room 2 and Room 4** is:
\[
\boxed{7x + 11}
\]

---

Would you like any more details or clarification on this solution?

Here are 5 related questions to deepen your understanding:
1. What would the expression be if Room 2 had different dimensions?
2. How does changing the value of \(x\) affect the total area?
3. Can you derive the total area if the dimensions of Room 1 were included?
4. How would you find the perimeter of Room 2 and Room 4?
5. What real-world applications can be drawn from solving for areas of different shapes?

**Tip:** Always remember that combining like terms is key to simplifying expressions!

Determine a simplified expression that represents the total area of Room 2 and Room 4.

This problem involves finding the total area of Room 2 and Room 4. Using the area formula for rectangles, the solution provides a step-by-step guide to simplify expressions. The dimensions of Room 2 and Room 4 are given, and their areas are calculated and combined to give the final expression.

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