This excellent solution came from Ruth from Manchester High School for Girls.

In the tetrahedron ABCD, let ABC and ACD be right angled. If you position the tetrahedron so that ABC is the base, then the vertex D is directly above the edge AC. This means that the height of the tetrahedron is the height of the triangle ACD which is

1 Ö2

and the area of the base of the tetrahedron is the area of the triangle ABC which is

1 2

. The volume of a pyramid is one third base times height. Therefore

V = 1 3 1 2 1 Ö2 = 1 6 Ö2 = Ö2 12