Gauss's Area Formula for Irregular Shapes

Abstract

To find the area of an irregular shape, we break the shape into common shapes. Then we find the area of each shape and add them, but this approach does not always work. In this paper we investigate Gauss’s area formula (for irregular shapes), also known as the shoelace formula or the shoelace algorithm. This theorem is outside the scope of school program. Nevertheless, we provide several applications that emphasize the importance and usefulness of this theorem. Most of the applications provided in this paper are created by the authors.