Notice that the square can be divided into four triangles of height 4cm and base 4cm:
The area of one of the triangles is:
![\begin{gathered} (1)/(2)b\cdot h=(1)/(2)(4\operatorname{cm})(4\operatorname{cm}) \\ =8cm^2 \end{gathered}]()
The area of the square is four times the area of one of the triangles:

Therefore, the area of the square is 32 squared centimeters.