Texas Instruments: Numb3 Rs: Irregular Polygon Centroids

Based off of the hit television show NUMB3RS, this lesson has students explore finding the centroid of an irregular polygon by finding the mean of the coordinates of the polygon's vertices. Further, students find the centroid given that the vertices are weighted (some vertices are more important than others), and finally, as an extension, students find the centroid of a region bounded by two functions (although this does require calculus, so the extension is best used in a calculus class; the normal lesson is still appropriate for lower classes).