A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?

Sliced

Age 14 to 16 Challenge Level

Slice the tetrahedron in two with a cut through the line $b$ and
one of the equal edges. The perpendiculars are very important
because of what you need to find the volume of a pyramid. You now
have two identical pyramids like this: