Similar Triangles

Call the side of the square  = x

Notice that  

 Δ ABE  ~  Δ  EGF

 Δ  EGF ~  Δ  FCD

So

 Δ  ABE ~  Δ FCD 

So

AB / BE   = FC / CD

28 / x  = x / 58   cross-multiply

x^2  = 58 * 28

x^2  = 1624  

So...the area of the square is 1624 units^2

Thank you Chris