When a figure is dilated by a scale factor, the effect on area can be described using the square of the scale factor. If the scale factor is less than 1 (indicating a reduction in size), the area of the dilated figure will be scaled by the square of the scale factor.
For instance, if the scale factor is \( k \) (where \( 0 < k < 1 \)), the area of the original figure will become \( k^2 \) times the original area after dilation. Since \( k^2 \) is a positive number less than 1, this means the area of the pentagon will decrease.
Moreover, the area decreases more rapidly than the lengths of the sides decrease because the lengths of the sides decrease by the factor \( k \), while the area decreases by the factor \( k^2 \).
So the correct response is:
The area decreases more rapidly than the lengths of the sides decrease.
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