Step #1 Stick a pin anywhere through the interior of the cardboard triangle. Pin the triangle loosely to a bulletin board. The triangle should be able to hang freely by its own weight.
Step #2 Tie a paper clip to a string and loop the string over the pin so that the weighted string hangs over the interior of the triangle. This string with a paper clip weight is a plumb line. Draw a line on the cardboard triangle, showing the path of the string.
Step #3 Stick the pin through another point in the interior of the triangle and hang the plumb line. Draw another line on the cardboard triangle, showing the new path of the string.
Step #4 The center of mass of the cardboard triangle is where the two lines cross. Check to see if your cardboard triangle balances on that point.
While the geometric construction and patty paper construction methods of finding the center of mass worked only for triangles, this physical procedure works for any cardboard polygon. Can you discover a geometric construction or patty paper construction method that locates the center of mass of a cardboard quadrilateral? (You could then use the plumb line method to check to see if your construction method works.)
"Discovering Geometry: An Inductive Approach" Serra, P. 165