How do i compute volume of a generic hexahedron with all its faces being quadrilateral?



I would compute the volume by first cutting the hexahedron into pieces.

Here is an example. In this figure I joined the point A to C, D, H and G to form a pyramid with base the quadrilateral CGHD and apex A. Remove this pyramid.

Now join A to F and remove the pyramid with quadrilateral base BFGC and apex A. Remove this pyramid.

What remains is a pyramid with quadrilateral EFGH as base and apex A.

Thus I have subdivided the hexahedron into three pyramids, each with a quadrilateral as its base and hence the volume of the hexahedron is the sum of the volumes of the three pyramids.

The volume of a pyramid is 1/3 x the area of the base x the height. Each base can be divided into two triangles to find its area and hopefully you have enough information about the hexahedron to find the heights of the pyramids.