Wondering if it is possible to estimate the surface area of a 2D shape where the only known value is the length of the enclosing boundary, and that it is know the internal surface area is solid. Really have no idea if it's possible, though if it is, what would be the most simple formula that would take the enclosing boundary as an input, and output the 2D shape's surface area?
It's not possible. You can get triangles of arbitrarily small area with a fixed perimeter. However, as you probably imagine, you cannot have arbitrarily large area with a fixed perimeter: see the isoperimetric inequality.