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.










