jmc

We are given the three side lengths of the triangle, so we can compute the perimeter of the triangle to be $6.2+8.3+9.5=24$. The square has the same perimeter as the triangle, so its side length is $\frac{24}{4}=6$. Finally, the area of the square is $6^2=36$, which is choice $\boxed{36{\text{ cm}}^2}$