What shapes can you make out of a triangle and a trapezium?

Answer 1

Assuming they don't overlap, and depending on their exact dimensions, these are some of the possible shapes:

A triangle (big)

A square

A rectangle

A parallelogram

A rhombus

A trapezium

A pentagon

A hexagon

A heptagon

and

if a vertex of the triangle rests on the side of the trapezium, an octagon.

a concave pentagon, a trapezium, a concave seven or eight sided figure (neither of the last two is a polygon but two polygons touching one another)