A pentagonal prism
One shape is the [quadrilateral] pyramid. Since this is a self-dual polyhedron, I cannot see what the other shape could be.
The shape you've described is a right pentagonal prism.
A right angled triangle is an example of a shape with exactly 2 perpendicular sides.
A right pentagonal prism.
trapezoid
A parallelogram.
parallelogram
a squareof course
X and T because the they can still make the T shape and still be perpendicular
A right angled triangle.
A capital "H."
rhombus