I haven’t got done listing kinds of trapezoids, of course. Arguably I’d never be able to finish, since, after all, couldn’t any possible length of the two bases — the parallel lines — and of different lengths of the diagonal legs be imagined? Well, perhaps, although a lot of those kinds are going to look the same. An isoceles trapezoid where the long base is 10 and the short base 8 looks a lot like one where the long base is 11 and the short base 7.5, at least if the bases are the same distance apart. But there are more cases imaginable.
I was ready to go with a little essay about how I ultimately figured out the area of a trapezoid, based on the formula for the area of triangles, when I realized that it was much easier to show this with a diagram. And I had a diagram drawn out pretty well, at least to the limits of my drawing ability and my power to use Photoshop Elements to do the drawing. But then it struck me that there’s a peril in using a diagram when you want to prove anything, and the nature of those perils deserved some attention.
Continue reading “Setting Out To Trap A Zoid”