To determine the area of a dilated figure, we can use the following formula:
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When a figure is dilated by a scale factor \( k \), the area of the new figure is given by the formula: \[ \text{Area}{\text{dilated}} = k^2 \times \text{Area}{\text{original}} \]
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In this case, the scale factor \( k = 3 \). Thus, \( k^2 = 3^2 = 9 \).
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Therefore, the area of the dilated figure will be 9 times the area of the original figure.
To find the correct answer, we need the area of the original figure (which is not provided in your question). However, if we denote the area of the original figure as \( A \), the area of the dilated figure would be:
\[ \text{Area}_{\text{dilated}} = 9A \]
Based on the options provided, you would match \( 9A \) with the possible answers:
- If \( A = 20 \), then \( \text{Area}_{\text{dilated}} = 180 \) (correct)
- If \( A = 45 \), then \( \text{Area}_{\text{dilated}} = 405 \) (incorrect)
- If \( A = 5 \), then \( \text{Area}_{\text{dilated}} = 45 \) (incorrect)
- If \( A = 30 \), then \( \text{Area}_{\text{dilated}} = 270 \) (incorrect)
Considering the option of 180 square units is correct if the original area was 20 square units. Without knowing the original area, the answer could be \( 180 \text{ square units} \) if this corresponds to a reasonable assumption based on the scale factor of 3.
Thus, if you can confirm that the area of the original figure is indeed 20 square units, then the answer would be:
180 square units.