To determine how dilation affects the area of a pentagon when the sides are dilated by a scale factor less than 1, we need to understand the relationship between linear dimensions (sides) and area.
When a shape is dilated by a scale factor \( k \) (where \( 0 < k < 1 \) in this case), the new area \( A' \) of the shape can be calculated using the formula:
\[ A' = k^2 \cdot A \]
where \( A \) is the original area.
Since \( k \) is less than 1, \( k^2 \) will also be less than 1. This means that the new area \( A' \) will be smaller than the original area \( A \). Specifically, because \( k^2 \) decreases more sharply than \( k \) itself (because squaring a number between 0 and 1 yields a smaller number), the area decreases more rapidly than the lengths of the sides.
Thus, the correct answer is:
a. The area decreases, more rapidly than the lengths of the sides decrease.