Some new geometrical properties, e.g., length, breadth and index of area coverage (IOAC) of a fuzzy set along with their computational aspects are introduced. An algorithm for providing both fuzzy and nonfuzzy segmentation based on these measures is also proposed. The proposed algorithm is found to be successful even for the input images containing multiple objects or an elongated object, where the existing fuzzy compactness based algorithm (which is valid for extracting a single compact object) fails. This is illustrated on various images.