When a two-dimensional shape is dilated by a factor of \( k \), the area of the shape is affected by the square of that factor.
If the dilation factor is \( k = 13 \), the effect on the area is calculated as follows:
\[ \text{New Area} = k^2 \times \text{Original Area} = 13^2 \times \text{Original Area} = 169 \times \text{Original Area} \]
Thus, the area is \( 169 \) times as great.
From the given options, the correct response is:
It is 169 as great.
However, since this option is not present, you might want to double-check the provided options. The other options do not seem to relate properly to the dilation factor of 13. If the dilation factor were \( 4 \) for example, then the area would be \( 16 \) times as great, but in this case, \( 13^2 \) is \( 169 \).