When a pentagon (or any geometric figure) is dilated by a scale factor less than 1, the lengths of the sides of the pentagon are reduced. Specifically, if a pentagon is dilated by a scale factor \( k \) (where \( 0 < k < 1 \)), each length of the sides is multiplied by \( k \).
The area of the pentagon, however, changes according to the square of the scale factor. Thus, if the area \( A \) of the original pentagon is transformed to an area \( A' \) under dilation by the factor \( k \), the relationship is given by:
\[ A' = k^2 \cdot A \]
Since \( k < 1 \), it follows that \( k^2 < 1 \). Therefore, \( A' < A \), indicating that the area of the pentagon decreases.
Furthermore, because the area scales by the square of the scale factor, the area decreases more rapidly than the side lengths of the pentagon. This is because the lengths of the sides only decrease by \( k \), while the area decreases by \( k^2 \).
Thus, the correct response is:
The area decreases more rapidly than the lengths of the sides decrease.
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