The pictured tetrahedron has four identical rectangular (i.e., right-angled or pythagorean) triangles as faces, with

AB=CD=p,
AC=BD=q,
AD=BC=r,
and p²+q²=r².

What's its volume, as a function of p, q and r?

I like Geometry a lot, but I'd never heard about such a tetrahedron! I already have half an answer: 1/6 times p times q times the height -- all I need now is the hegith and I'm done!  ;-)

Posted by Oskar on 2004-04-26 09:28:51