To find the area of the dilated figure, we first need to determine the area of the original composite figure and then apply the scale factor of 3.
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Calculate the area of the original figure: If the dimensions of the rectangles were provided in the image you mentioned, you would calculate the area of each rectangle and then add them together to get the total area of the composite figure.
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Dilate the area by the scale factor: When a figure is dilated by a scale factor \( k \), the area scales by a factor of \( k^2 \). Therefore, if the original area is \( A \):
\[ \text{Area of dilated figure} = A \times k^2 \] For a scale factor of 3:
\[ \text{Area of dilated figure} = A \times 3^2 = A \times 9 \]
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Select the correct answer: You need to multiply the original area by 9 to find the area of the dilated figure.
If you had the original area calculated, just multiply that number by 9 to get the answer. Without the original measurements, the exact area cannot be determined. If the original area was one of the options listed (e.g., 30 square units), for example, then:
\[ 30 \times 9 = 270 \text{ square units} \]
From your options, if the original area is 30 square units, the area after dilation would be 270 square units.
Please check the original area from the image to confirm. Based on common problems, if the original area was indeed 30 square units, the correct answer would be 270 square units.
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