4) Look at this square: (1) If the side lengths are halved, then which of the following statements about its area will be true? (1) The ratio of the new area to the old area will be $1: 4$. The ratio of the new area to the old area will be $1: 8$. The ratio of the new area to the old area will be $9: 1$. The ratio of the new area to the old area will be $1: 2$.

Step 1 ：Let the original side length be \(s\), then the new side length is \(\frac{s}{2}\).

Step 2 ：Calculate the area of the original square and the new square: \(s^2\) and \(\left(\frac{s}{2}\right)^2\).

Step 3 ：Find the ratio between the new area and the old area: \(\frac{\left(\frac{s}{2}\right)^2}{s^2}\).

Step 4 ：Simplify the ratio: \(\frac{\frac{s^2}{4}}{s^2}\) = \(\frac{1}{4}\).

Step 5 ：\(\boxed{1:4}\) is the ratio of the new area to the old area.