PaperJS: Join multiple path objects to create a single path object

Question

Lets say I have multiple path objects of various shapes and sizes, that intersect with one another, like those in the [Hit Testing example][1]. Assuming I have a few of them selected at the same time, how could I join them together into a single path element, eliminating the overlapping path points, to create a new shape. For the sake of simplicity, let's apply the fill from the topmost shape.