[tex]\displaystyle\\
\text{Notatii:}\\
D=\text{Diametrul cercului}\\
R=\text{Raza cercului}=4~cm\\
d=\text{diagonala patratului}\\
l=\text{latura patratului}\\
P=\text{Perimetrul patratului}\\
A=\text{Aria patratului}\\\\
\text{Rezolvare:}\\\\
d=D=2R=2\times4=\boxed{8~cm}\\\\
l=\frac{d}{\sqrt{2}}=\frac{8}{\sqrt{2}}=\frac{8\sqrt{2}}{2} =\boxed{4\sqrt{2}~cm}\\\\
P=4\times l=4\times4\sqrt{2}=\boxed{16\sqrt{2}~cm}\\\\
A=l^2=(4\sqrt{2})^2=16\times2=\boxed{32~cm^2}[/tex]
