scale: 1 inch to 8 feet
actual area: 256 square feet
scale: 1 inch to 4 feet
actual area: 128 square feet
scale: 1 inch to 7 feet
actual area: 147 square feet
scale: 1 inch to 5 feet
actual area: 225 square feet
area of scale drawing
scale and actual area
scale drawing area:
4 square inches
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scale drawing area:
8 square inches
arrowRight
scale drawing area:
9 square inches
arrowRight
scale drawing area:
3 square inches
arrowRight


To find the actual area of a scale drawing, we can use the relationship between the scale factor and the actual area. Here, we have the scale, actual area, and the area of the scale drawing. We will calculate the scale drawing area given the actual area and the scale, and then verify if the actual area matches the given values.

### Scale: 1 inch to 8 feet
Actual area: 256 square feet
\[
\text{Scale factor} = 8 \, \text{feet per inch}
\]
\[
\text{Scale drawing area} = \left(\frac{\text{Actual area}}{(\text{Scale factor})^2}\right)
\]
\[
\text{Scale drawing area} = \frac{256}{8^2} = \frac{256}{64} = 4 \, \text{square inches}
\]

### Scale: 1 inch to 4 feet
Actual area: 128 square feet
\[
\text{Scale factor} = 4 \, \text{feet per inch}
\]
\[
\text{Scale drawing area} = \frac{128}{4^2} = \frac{128}{16} = 8 \, \text{square inches}
\]

### Scale: 1 inch to 7 feet
Actual area: 147 square feet
\[
\text{Scale factor} = 7 \, \text{feet per inch}
\]
\[
\text{Scale drawing area} = \frac{147}{7^2} = \frac{147}{49} = 3 \, \text{square inches}
\]

### Scale: 1 inch to 5 feet
Actual area: 225 square feet
\[
\text{Scale factor} = 5 \, \text{feet per inch}
\]
\[
\text{Scale drawing area} = \frac{225}{5^2} = \frac{225}{25} = 9 \, \text{square inches}
\]

Therefore, the areas of the scale drawings are:
1. 4 square inches
2. 8 square inches
3. 3 square inches
4. 9 square inches

Do you want details or have any questions?

Here are 5 questions you can ask next:
1. How do you determine the dimensions of a scale drawing given its area and scale factor?
2. How does changing the scale factor affect the area of a scale drawing?
3. Can you explain how to convert between different units of measurement in scale drawings?
4. What are some common applications of scale drawings in architecture and engineering?
5. How do you calculate the dimensions of a scale drawing from the actual dimensions?

**Tip:** When working with scale drawings, always ensure you square the scale factor when converting between actual areas and scale drawing areas.

Learn how to solve scale drawing problems by finding scale drawing areas. This problem involves determining scale factors and using proportions to calculate the scale drawing areas. Suitable for students in Grades 6-8.

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