The answer is the polygon corresponding to the merged convex hulls.
More efficient algorithms exist, and involve finding the bridges between the polygons.
Given two disjoint polygons, there exist two bridges between the polygons. Two intersecting convex polygons. There are eight bridges joining eight vertices. This applies to polygons as well. A very simple way to obtain the convex hull of a set of points is to divide the point set in two, and recursively compute the convex hulls of the two new smaller sets, and then merge them.