To find the area of the dilated rectangle, we first need to determine the dimensions of the original rectangle and then apply the scale factor to them.
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Original dimensions:
- Height = 6 inches
- Base (width) = 8 inches
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Area of the original rectangle: \[ \text{Area} = \text{Height} \times \text{Base} = 6 , \text{inches} \times 8 , \text{inches} = 48 , \text{square inches} \]
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Applying the scale factor: The scale factor is 0.5, which means each dimension will be multiplied by 0.5:
- New height = \( 6 \times 0.5 = 3 \) inches
- New base = \( 8 \times 0.5 = 4 \) inches
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Area of the dilated rectangle: \[ \text{Area} = \text{New Height} \times \text{New Base} = 3 , \text{inches} \times 4 , \text{inches} = 12 , \text{square inches} \]
The area of the dilated rectangle is 12 square inches.