The trapezoidal rule is actually from calculus. A little above the geometry level, the basic idea of it would be quite understandable to a geometry student.
Another interesting one is the Mars Rover which contain the Rover's solar panels. I believe they are in the shape of a trapezoid because the panels are initially folded up against the Rover. The trapezoid shape is best for that unfolding transition.
I don't have specific info on most of the others. They're just trapezoids out in the real world.