It is better to see this property if you stay with parallelograms and use the Cavalieri Principle. Here is [page][1] with an animation showing what I mean (clink on the link and accept).


There is also a demonstration of the first formula using triangles and again using only Cavalieri. There was an animation "proof without words" for it in the site "art of problem solving" but I can't find it anymore. 
 


  [1]: http://matematica-para-todos.wikispaces.com/Propriedade+de+Determinante+por+Cavalieri