In this paper, we examine the problem of efficiently computing a class of aggregate functions on regions of space. We first formalize region-based aggregations for a large class of efficient geometric aggregations. The idea is to represent the query object with pre-defined objects with set operations, and compute the aggregation using the pre-computed aggregation values. We first show that it applies to existing results about points and rectangular objects. Since it is defined using set theory instead of object shapes, it can be applied to polygons. Given a database D of polygonal regions, a tessellation T of the plane, and a query polygon q constructed from T, we prove that the aggregation of q can be calculated by the aggregation over triangles and lines constructed from segments and vertices in q, which can be pre-computed. The query time complexity is O(klogn), where k is the size of query polygon and n is the size of T.