Relative to a fixed origin \(O\), the points \(A\), \(B\), \(C\) and \(D\) have coordinates \(( 0,4,1 ) , ( 4,0,0 )\), \(( 3,5,2 )\) and \(( 2,2 , k )\) respectively, where \(k\) is a constant.
Determine the exact area of triangle \(A B C\).
Determine in terms of \(k\), the volume of the tetrahedron \(A B C D\), simplifying your answer. \(( 3,5,2 )\) and \(( 2,2 , k )\) respectively, where \(k\) is a constant.
Determine the exact area of triangle \(A B C\).
$$\text { etrahedron } A B C D \text {, simplifying }$$