I have been dissatisfied with the area postulate generally in use these days, that the area of a square = the side squared. I have formulated an alternative postulate, which I believe is more helpful. It is that, of two rectangles with the same width but different lengths, the ratio of the areas contained = the ratio of the lengths. From this, the area formulae for the rectangle and square can be derived. I have posted the details on my website at http://www.petersnewyork.com/postulate.html. I feel this postulate is more self-evident than accepting the area of the square as the side squared, and it is sufficient for deriving all the area formulae.
