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