The areas of squares form an IGP

$a_1 = A_1 = 10^2 ~ \text{m}$

$r = \left( \dfrac{5\sqrt{2}}{10} \right)^2 = 1/2$

Note: All squares are similar; and for similar figures

$$\dfrac{A_2}{A_1} = \left( \dfrac{x_2}{x_1} \right)^2 = r ~ \text{of GP}$$

where *x*_{1} and *x*_{2} = corresponding linear dimensions

$S = \dfrac{a_1}{1 - r} = \dfrac{10^2}{1 - 1/2}$

$S = 200 ~ \text{m}^2$ ← *answer*