Using the square of the scale factor to calculate the area of a dilated figure is important because the scale factor represents the ratio of the corresponding sides of the pre-image and the image. This means that each side of the pre-image is multiplied by the scale factor to get the corresponding side of the image.
When we calculate the area of a figure, we are dealing with two-dimensional measurements. The area is a measure of how much space the figure occupies. Since the area is calculated by multiplying the length of one side by the length of another side, it is influenced by both dimensions.
When we dilate a figure, we are enlarging or shrinking it, but we are also changing both dimensions by the same scale factor. Therefore, the area of the dilated figure will not just be the scale factor multiplied by the area of the pre-image. Instead, the area will be affected by the change in both dimensions, resulting in a new area.
By using the square of the scale factor to calculate the area of a dilated figure, we are taking into account the change in both dimensions. Since both dimensions are multiplied by the same scale factor, squaring it ensures that both dimensions are squared as well. This results in a proportionate change in the area.
) Explain the importance of using the square of the scale factor to calculate the area of a dilated figure.
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