How many Permutation of non overlapping Elements inside an area?

Question

I have the following case:

• An area divided into cells, so f.e. $6 \times 6 = 36$ cells.
• A concrete number of Elements which need to fit into this area, f.e.
  6. Elements can span 1 to N cells.
• Each element has an area, f.e. $\{3, 6, 4, 5, 6, 12\}$, so that the total area is again the overall ($36$).

And here my question:

1. How do I calculate row / colums (or height/width) of the elements: for an area of 6, the different options could for example be $6 \times 1, 1 \times 6, 3 \times 2 \text{ and } 2 \times 3 ..$ A necessary condition is that elements need to be a square or a rectangle, so f.e. not an U or T-shape occupying the grid in the cells.
2. How do I calculate how many possible options I have to position those elements inside the area?

Example layout

Many thanks!