For a right tetrahedron with verticies (0,0,0), (a,0,0),
(0,b,0), and (0,0,c), the base of the "hypotenuse" is 
B = sqrt(a^2 + b^2) and the height is H = sqrt(c^2 + h^2) 
where (by similar triangles) h = ab/B is the distance from
the origin to the base, so we have

   Area^2 = (HB/2)^2 = (ab/2)^2 + (ac/2)^2 + (bc/2)^2