https://file.aiquickdraw.com/mathbot/file/1725975004220poqhys5q.jpg

Let's analyze the problem shown in the image.

### Given information:
- **Blueprint scale**: \(6 \, \text{cm} = 15 \, \text{ft}\)
- There is a room on the blueprint with dimensions labeled "2 cm" and "4 cm."
- The room with the question mark has no dimensions labeled.

### Step-by-step approach:
1. **Find all necessary dimensions on the blueprint:**
   - The larger room next to the one marked with a question mark has dimensions \(8 \, \text{cm} \times 4 \, \text{cm}\).
   - The vertical length next to the question mark room is the same as the adjacent room (which is 4 cm wide).

2. **Determine missing lengths:**
   - The length for the top side of the question mark room is the remaining width after subtracting from the 8 cm. Since the room on the left takes 2 cm, the remaining width is \(8 - 2 = 6 \, \text{cm}\).
   - So, the dimensions of the question mark room are \(6 \, \text{cm} \times 4 \, \text{cm}\).

3. **Find the area of the room in real life using the scale:**
   - First, calculate the blueprint area: \( \text{Area} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2 \).
   - Now, convert this to the actual area in feet. Since \(6 \, \text{cm} = 15 \, \text{ft}\), we need to scale the dimensions:
     - \(1 \, \text{cm} = \frac{15}{6} \, \text{ft} = 2.5 \, \text{ft}\)
     - The actual dimensions of the room are \(6 \, \text{cm} \times 2.5 = 15 \, \text{ft}\) and \(4 \, \text{cm} \times 2.5 = 10 \, \text{ft}\).
   - The actual area is \( 15 \, \text{ft} \times 10 \, \text{ft} = 150 \, \text{ft}^2 \).

Thus, the actual area of the room with the question mark is **150 square feet**.

Would you like further explanation, or do you have any questions?

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Here are some related questions to explore:
1. How does scaling affect perimeter calculations for geometric shapes?
2. If the blueprint scale changed, how would that affect the calculated area?
3. What are the dimensions of the entire floor in the blueprint and real life?
4. How would you calculate the area if the room shapes were irregular?
5. How can you calculate the volume of a room given its height and floor area?

**Tip**: Always double-check units when scaling diagrams to avoid confusion between actual and blueprint measurements.

Determine the actual area of the room marked with a question mark, given the blueprint scale of 6 cm = 15 ft.

Learn how to calculate the actual area of a room on a blueprint using a scale of 6 cm = 15 ft. This problem demonstrates the process of determining dimensions and converting scaled measurements into real-life dimensions. Suitable for students in Grades 7-9.

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