To find the area of the dilated rectangle, we first need to calculate the area of the original rectangle. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{height} \times \text{base} \]
For the original rectangle:
- Height = 6 inches
- Base = 8 inches
Calculating the area of the original rectangle:
\[ A = 6 , \text{inches} \times 8 , \text{inches} = 48 , \text{square inches} \]
Next, we apply the dilation. When a shape is dilated by a scale factor of \( k \), the new dimensions become:
- New height = \( 6 \times 0.5 = 3 \) inches
- New base = \( 8 \times 0.5 = 4 \) inches
Now, we calculate the area of the dilated rectangle:
\[ A_{\text{dilated}} = \text{new height} \times \text{new base} = 3 , \text{inches} \times 4 , \text{inches} = 12 , \text{square inches} \]
Thus, the area of the dilated rectangle is \( \boxed{12} \) square inches.
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