To find the area of the actual house, you can follow these steps:

1. Determine the area of the floor plan: The area of the floor in the plan is given by the formula: $\text{Area of the floor plan} = \text{Length} \times \text{Width}$ Substituting the given values: $\text{Area of the floor plan} = 20 \, \text{cm} \times 13 \, \text{cm} = 260 \, \text{cm}^2$

2. Calculate the area of the actual house: The linear scale factor is given as 50. Since the area scales by the square of the linear scale factor, the area of the actual house is: $\text{Area of the actual house} = \text{Area of the floor plan} \times (\text{Scale Factor})^2$ Substituting the values: $\text{Area of the actual house} = 260 \, \text{cm}^2 \times 50^2 = 260 \, \text{cm}^2 \times 2500 = 650,000 \, \text{cm}^2$

3. Convert the area to square meters: Since the area is currently in square centimeters, convert it to square meters: $650,000 \, \text{cm}^2 = \frac{650,000}{10,000} \, \text{m}^2 = 65 \, \text{m}^2$

So, the area of the actual house is 65 square meters.

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert between square centimeters and square meters?
2. What is the significance of a scale factor in architectural drawings?
3. How would the area change if the scale factor was 100 instead of 50?
4. How can you verify the accuracy of a scaled model?
5. How do you calculate the perimeter of the actual house given the scale factor?
6. What are some common uses of scale factors in real-world applications?
7. How would the dimensions of the house in meters be calculated using the scale factor?
8. How would the area change if only one dimension was scaled differently?

Tip: When working with scale factors, remember that the area scales by the square of the linear scale factor,