When a two-dimensional shape is dilated by a factor of \( k \), the area of the shape changes by a factor of \( k^2 \).
In this case, the dilation factor is \( \frac{1}{3} \). To find the effect on the area, we calculate:
\[ \left( \frac{1}{3} \right)^2 = \frac{1}{9} \]
This means that the new area will be \( \frac{1}{9} \) of the original area.
Therefore, the correct response is: It is \( \frac{1}{9} \) as great.