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

An irregular tetrahedron has two opposite sides the same length
($a$ say) and the line joining their midpoints is perpendicular to
these two edges and is of length $b$. What is the volume of the
tetrahedron?