Question

Marc draws a rectangle with a height of 6 inches and a base of 8 inches. He dilates the figure using a scale factor of 0.5, or 1/2. What is the area of the dilated rectangle?
The area of the dilated rectangle is _ square inches

Answer 1

To find the area of the dilated rectangle, we first need to compute the area of the original rectangle and then apply the scale factor.

1. **Calculate the area of the original rectangle:**
\[
\text{Area} = \text{height} \times \text{base} = 6 \, \text{inches} \times 8 \, \text{inches} = 48 \, \text{square inches}
\]

2. **Dilate the dimensions using the scale factor of 0.5:**
- New height:
\[
\text{New height} = 6 \, \text{inches} \times 0.5 = 3 \, \text{inches}
\]
- New base:
\[
\text{New base} = 8 \, \text{inches} \times 0.5 = 4 \, \text{inches}
\]

3. **Calculate the area of the dilated rectangle:**
\[
\text{Area of dilated rectangle} = \text{new height} \times \text{new base} = 3 \, \text{inches} \times 4 \, \text{inches} = 12 \, \text{square inches}
\]

Therefore, the area of the dilated rectangle is **12 square inches**.