https://file.aiquickdraw.com/mathbot/file/1726499038216jxumu8n6.jpg

The problem asks for the area of a rectangle that has been dilated by a scale factor of 4. Here's the solution process:

1. **Original Rectangle Dimensions**:
   - Length: \( 3 \, \text{inches} \)
   - Width: \( 2 \, \text{inches} \)

2. **Area of the Original Rectangle**:
   The area \( A_{\text{original}} \) of the original rectangle is:
   \[
   A_{\text{original}} = \text{Length} \times \text{Width} = 3 \, \text{inches} \times 2 \, \text{inches} = 6 \, \text{square inches}
   \]

3. **Dilated Dimensions**:
   The scale factor is 4, so both the length and width are multiplied by 4:
   - Dilated length: \( 3 \times 4 = 12 \, \text{inches} \)
   - Dilated width: \( 2 \times 4 = 8 \, \text{inches} \)

4. **Area of the Dilated Rectangle**:
   The area \( A_{\text{dilated}} \) of the dilated rectangle is:
   \[
   A_{\text{dilated}} = 12 \, \text{inches} \times 8 \, \text{inches} = 96 \, \text{square inches}
   \]

So, the area of the resulting figure is **96 square inches**, which matches the first option.

Would you like further details or have any other questions?

Here are 5 related questions:
1. What happens to the perimeter when a figure is dilated by a scale factor?
2. If the scale factor were 2, what would be the new area?
3. How does the scale factor affect the area of a figure in general?
4. How do you calculate the area of a triangle when it's dilated by a scale factor?
5. What is the difference between linear dilation and area dilation?

**Tip**: When dilating a shape, the area increases by the square of the scale factor.

If the side lengths of the figure in the diagram are dilated by a scale factor of 4, what is the area of the resulting figure?

Calculate the area of a rectangle after it is dilated by a scale factor of 4. The original dimensions are 3 inches by 2 inches, and the resulting area is 96 square inches. Learn the step-by-step solution to understanding dilations and area calculation.

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