Question 1183430
The area of the parallelogram is just the magnitude of the cross product of the vectors spanning the parallelogram.  
The vector from the point (1,1,1) to (4,4,4) is <3,3,3>. The vector from (1,1,1) to (8,-3, 14) is <7,-4,13>.  Hence the area of the parallelogram is 


{{{abs(abs(matrix(3,3, i,j,k, 3,3,3,7,-4, 13))) = abs(abs(39i + 21j -12k -(21k-12i+39j))) = abs(abs(51i - 18j - 33k)) = sqrt(51^2+(-18)^2+(-33)^2) = 3*sqrt(446) = 63.36}}}, to 2 d.p.