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 \( \frac{1}{3} \). To find the effect on the area, we calculate:
\[ \text{New Area} = \text{Original Area} \times \left(\frac{1}{3}\right)^2 = \text{Original Area} \times \frac{1}{9} \]
This means the new area is \( \frac{1}{9} \) as great as the original area.
Thus, the correct response is:
It is \( \frac{1}{9} \) as great.