Suppose that each of the smaller rectangles has a longer side of length $x \mathrm{~cm}$ and a shorter side of length $y \mathrm{~cm}$. Since the perimeter of each of the rectangles is 40 cm, then $2x+2y=40$ or $x+y=20$. But the side length of the large square is $x+y \mathrm{~cm}$. Therefore, the area of the large square is $(x+y)^{2}=20^{2}=400 \mathrm{~cm}^{2}$.