Larryhaskell,
You asked how we hand sketchers calculated arcs? As with the imaginary rectangles and squares, you must envision the imaginary piece of pie, half circle, what have you. 3.14 (pi) X radius, squared gives you the entire circle. You then divide that figure by the portion of full circle that exists. If it's a small arced window rather than an angled bay with just a minute slice of the circle, those threw that calulation out the window. I would measure the hieght of the arc (from flat wall to deepest point of the arc) and then the length of the arc. Now then for the honest to God truth, I didn't pull out my geometry manual, nor protractor and mess with chord, degrees of arc, etc. I resketched the arc on a scratch area of graph paper. I enclosed the sketched arc area in a rectangle the same hieght and depth, then counted the 'blank' squares and portions of blanks. This blank portion gave me a percetange figure to deduct from the area of the imaginary rectangle, and bingo. The remaining area was darn close to actual SF. Not exactly scientific, but well within acceptable accuracies.
Any wonder why I like the Apex so much better???