The question "What shape will have the largest area for a given perimeter?" identifies an important relationship between area and perimeter that has long been intuitively realized in many cultures. Historically, numerous cultures have made use of this relationship between area and perimeter when struggling to build dwellings with shapes that maximized floor space. Since perimeter is limited by the available materials, determining what shape will have the largest area is very important to people who find materials difficult to work with or hard to obtain. Therefore, mathematics is integrally related to social studies and architecture. The purpose of the activity described in this article is to go beyond intuition and instill a conceptual understanding of relationships between area and perimeter. Using Geometer's Sketchpad software facilitates pattern finding, and affords students the means to draw figures and calculate area and perimeter quickly and simultaneously. This tool also allows students to make conjectures, express their thoughts, verify their ideas, test their conjectures, and make generalizations and connections-all skills that are essential for students to become competent solvers of inquiry problems. This classroom activity was highly successful with eighth-grade students in a first-year algebra class. (Contains 7 figures and 4 tables.) (JDL)