In[405]:=

areaUS[{xn[1], yn[1], z[1]}, {xn[2], yn[2], zn[2]}, {xn[3], yn[3], zn[3]}] // Simplify

Out[405]=

1/4 √ (-(((xn[1] - xn[2])^2 + (yn[1] - yn[2])^2 + (z[1] - zn[2])^2)^(1/2) - ((xn[1] - xn[3])^2 + (yn[1] - yn[3])^2 + (z[1] - zn[3])^2)^(1/2) - ((xn[2] - xn[3])^2 + (yn[2] - yn[3])^2 + (zn[2] - zn[3])^2)^(1/2)) (((xn[1] - xn[2])^2 + (yn[1] - yn[2])^2 + (z[1] - zn[2])^2)^(1/2) + ((xn[1] - xn[3])^2 + (yn[1] - yn[3])^2 + (z[1] - zn[3])^2)^(1/2) - ((xn[2] - xn[3])^2 + (yn[2] - yn[3])^2 + (zn[2] - zn[3])^2)^(1/2)) (((xn[1] - xn[2])^2 + (yn[1] - yn[2])^2 + (z[1] - zn[2])^2)^(1/2) - ((xn[1] - xn[3])^2 + (yn[1] - yn[3])^2 + (z[1] - zn[3])^2)^(1/2) + ((xn[2] - xn[3])^2 + (yn[2] - yn[3])^2 + (zn[2] - zn[3])^2)^(1/2)) (((xn[1] - xn[2])^2 + (yn[1] - yn[2])^2 + (z[1] - zn[2])^2)^(1/2) + ((xn[1] - xn[3])^2 + (yn[1] - yn[3])^2 + (z[1] - zn[3])^2)^(1/2) + ((xn[2] - xn[3])^2 + (yn[2] - yn[3])^2 + (zn[2] - zn[3])^2)^(1/2)))


Converted by Mathematica  (March 7, 2003)