When a two-dimensional shape is dilated by a scale factor, the area of the shape changes by the square of that scale factor.
If the scale factor is 3, then you calculate the change in area as follows:
\[ \text{New Area} = \text{Original Area} \times (\text{Scale Factor})^2 = \text{Original Area} \times 3^2 = \text{Original Area} \times 9 \]
Therefore, the area will be 9 times as great.
So, the correct response is: The area will be 9 times as great.