This challenge is very straightforward. Given four 3-dimensional points, calculate the surface area of the tetrahedron that they form. This is code-golf, so shortest code wins. Standard loopholes apply, with the added stipulation that any built-in function to do this task given four points is prohibited.
You can assume all four points will be distinct, and will be given via STDIN, 1 point per line. Each point will consist of three 16-bit unsigned integers. The exact format of each point can be modified if it makes things easier, such as three space separated integers. Having each point on a separate line is mandatory however. Output should be through STDOUT, to at least 2 decimal places.
For those of you who do not know, a tetrahedron is a 3-d solid, formed by 4 triangular faces.
# input (format is up to you, see clarification above) [23822, 47484, 57901] [3305, 23847, 42159] [19804, 11366, 14013] [52278, 28626, 52757] # output 2932496435.95
Please leave a note if you notice my math is wrong.