If the diagonal of a square is doubled, then the area of the square will be:

The area of a square in terms of its diagonal $d$ is given by:
$$\text{Area}=\frac{d^2}{2}$$
If the diagonal is doubled ($d^{\prime }=2d$), the new area will be:
$${\text{Area}}^{\prime }=\frac{(2d{)}^2}{2}=\frac{4d^2}{2}=4\times \text{Area}$$
Hence, the area becomes four times the original area.