The diagonal of the square will be the hypotenuse of an isosceles right triangle, two sides of which are sides of the square.

So, if I call each side of the square x, then using the Pythagorean theorem:

$x^{2} + x^{2} = (14.1)^{2}$

$2x^{2} = (14.1)^{2}$

Taking the square root of both sides:

$\sqrt{2}x = 14.1$

Divide by the square root of 2:

$x = \frac{14.1}{\sqrt{2}}$

Now that we have x, one side of the square, we can find the area, x²:

$x^{2} = \frac{(14.1)^{2}}{2}$

Using a calculator, (14.1)² = 198.81. Divided by 2 we get 99.405. That rounds down to the nearest integer, 99.

Alternatively, we might know that an isosceles right triangle is a 45-45-90 triangle whose sides have the ratio $x:x:\sqrt{2}x$. Since the hypotenuse is 14.1, then $\sqrt{2}x = 14.1$. Divide both sides by $\sqrt{2}$ and we get $x = \frac{14.1}{\sqrt{2}}$. Then we can proceed as above.