ToT 2019-spring SA5

The orthogonal projection of a tetrahedron onto a plane containing one of its faces is a trapezoid of area $1$ , which has only one pair of parallel sides. a) Is it possible that the orthogonal projection of this tetrahedron onto a plane containing another its face is a square of area $1$ ? b) The same question for a square of area $1/2019$ .

(Mikhail Evdokimov)