Question 3

Given an acute angled triangle \(T\), show that there is a unique tetrahedron whose faces are all congruent to \(T\) and find the volume of this tetrahedron.

Partial Solution by Billy Smells

Let our acute triangle have side lengths \(a\), \(b\) and \(c\).

a triangle

We can construct a net for the tetrahedron, as shown below:

a tetrahedron net