We continue the study in part I of geometric properties of self similar and self a ne tiles We give some experimental results from implementing the algorithm in part I for computing the dimension of the boundary of a self similar tile and we describe some conjectures that result We prove that the dimension of the boundary may assume values arbitrarily close to the dimension of the tile We give a formula for the area of the convex hull of a planar self a ne tile We prove that the extreme points of the convex hull form a set of dimension zero and we describe a natural gauge function for this set Introduction to Part II This paper is a continuation of SW which we refer to as part I and the sections are numbered accordingly In Section of part I we obtained an algorithm for computing the dimension box and Hausdor dimensions are equal of the boundary in the case of a self similar tile satisfying