https://file.aiquickdraw.com/mathbot/file/1726185607339rnmf5imn.jpg

Let's analyze and solve the problems given in the image.

1. **Draw a scaled copy of polygon Q using a scale factor of 2:**
   
   To scale the polygon by a factor of 2, multiply each side length of the original polygon by 2. The given polygon Q seems to be a rectangle with dimensions 4 units by 1 unit.

   Original dimensions:
   - Length: 4 units
   - Width: 1 unit

   Scaled dimensions:
   - Length: \(4 \times 2 = 8\) units
   - Width: \(1 \times 2 = 2\) units

   The scaled polygon will be a rectangle with dimensions 8 units by 2 units.

2. **What is the area of the scaled copy?**

   The area \(A\) of a rectangle is given by the formula:
   \[
   A = \text{Length} \times \text{Width}
   \]

   For the scaled polygon:
   \[
   A = 8 \, \text{units} \times 2 \, \text{units} = 16 \, \text{square units}
   \]

3. **Complete the table for different scaled copies of polygon Q:**

   To complete the table, we need to calculate the dimensions and areas for different scale factors.

   - **Scale factor: 1** (original polygon)
     - Dimensions: 4 units by 1 unit
     - Area: \(4 \times 1 = 4\) square units
     
   - **Scale factor: 2** (already calculated)
     - Dimensions: 8 units by 2 units
     - Area: \(8 \times 2 = 16\) square units
   
   - **Scale factor: 3**
     - Dimensions: \(4 \times 3 = 12\) units by \(1 \times 3 = 3\) units
     - Area: \(12 \times 3 = 36\) square units
   
   - **Scale factor: 4**
     - Dimensions: \(4 \times 4 = 16\) units by \(1 \times 4 = 4\) units
     - Area: \(16 \times 4 = 64\) square units

Would you like to go through any of the steps in more detail or have any specific questions?

Here are some related questions that could expand your understanding:

1. How would the perimeter of the scaled polygon change with a scale factor of 3?
2. If the original polygon was a different shape, such as a triangle, how would the scaling process differ?
3. What happens to the area of the polygon if the scale factor is less than 1 (e.g., 0.5)?
4. Can you generalize the relationship between the scale factor and the area of the polygon?
5. How does the concept of scaling apply to real-world scenarios, such as map reading or model building?

**Tip:** When scaling a figure, remember that all linear dimensions (length, width, height) are multiplied by the scale factor, but the area is multiplied by the square of the scale factor.

Draw a scaled copy of polygon Q using a scale factor of 2. What is the area of the scaled copy? Complete the table for different scaled copies of polygon Q.

Learn how to scale a polygon by a factor of 2 and calculate the area of the scaled copy. This geometry problem demonstrates key concepts in scaling and area, including a step-by-step guide to drawing and calculating the dimensions of the scaled polygon. Ideal for students in Grades 6-8.

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