When a two-dimensional shape is dilated by a factor of \( k \), the area of the shape is affected by a factor of \( k^2 \).
If the shape is dilated by a factor of \( \frac{1}{3} \), the effect on the area can be calculated as follows:
\[ \text{Area factor} = k^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9} \]
This means that the new area will be \( \frac{1}{9} \) of the original area. Therefore, the area of the shape is reduced to one-ninth of its original area when dilated by a factor of \( \frac{1}{3} \).