One strategy to approach this problem is to first find the center of mass of the polygon. The next step would be to move the problem forward in time, exactly to the point where the polygon hits the surface.
At this point in you can look at the problem as a rotation of the polygon around it's lower left corner, i.e. you can treat that part with the concept of angular momentum.
Once the lower right corner of the polygon hits the ground, it's impulse gets reflected by the wall and it starts bouncing off again. At the same time, the centre of the rotation is moved from the lower left corner to the lower right corner of the polygon and the sign of the rotation is changed.
So the equation of motion of the polygon is now governed by the reflected impulse that is superimposed by a torque.
To put this in equations is probably not easy and will require some playing around.