Letters; February/March 2007; Scientific American Mind; by Staff Editor; 2 Page(s)
I enjoyed reading "The Eureka Moment," by Guenther Knoblich and Michael Oellinger. The authors give a puzzle ("Puzzle Two") with the objective of having readers calculate the combined area of a square and a parallelogram. The solution given (that is, treating the figure as two overlapping triangles) is creative. But I am not certain of its advantage over standard geometric computation.
We are told that the figures are a parallelogram and a square. The formula for the area of a parallelogram is the product of the length of the base and the (perpendicular) height. A glance at the diagram shows b to be the length corresponding to one side of the square plus the length of the base of the parallelogram, so the length of the base is clearly b - . The height of the parallelogram is already labeled a, so that makes the area of the parallelogram a(b - a) or ab - a2. The area of the square is of course the second power of the length of a side a, so it is a2. Summing these two areas gives ab - a2 + a2, which is equal to ab, the desired answer.