3D matrices

A tetrahedron T has been transformed and its vertices are now
( root2, 0,0) , (root 2,1,00, (0, 2,3root2) and (0,0,0) Find its volume. I am given that the formula is (1/3)x (area of base) x height.

I have the area as root 2 x 1 and the height as 3root2. (I tried to draw it) but the answer in the book is

Area of base on plane z = (1/2) x (root 2) x 1
I have no idea where any of that comes from.

Help, please, if you can.

Thanks

The area of the base is just the area of a triangle with perpendular sides sqrt(2) and 1 (origin and first two points). Hnece the 1/2 multtiplier.

Edit - Dont know what the books says, but it should just be 1/6 of the det of the matrix, which as the first row has two zero elements, is easy to evaluate.