Irregular Shape Area for Dummies

If there's one geometry problem that confuses people more than any others, it's apparently how to calculate the area of an irregular shape. We've seen this one a couple of times before in the eHow.com back list, and the answer is invariably some form of "break it into regular shapes." That's all well and good, except what is someone going to do with a shape like the one at the right? That's one hell of a lot of "regular shapes," not to mention that it has a rather randomly curved edge. Nonetheless, when assigned to rewrite "How To Calculate The Area of an Irregular Shape" for Sciencing.com, rewrite specialist Lisa Maloney fell back on the tried and... well, not "true"; perhaps the "tried and simplistic"?

We'll be honest here: Maloney's solution is perfectly useful for a shape that is only a little irregular. You can use it for polygons shaped like an L or an H, both of which are simple combinations of rectangles. It also works for a polygon that looks like a child's version of a house; a square with a triangle on top. In fact, it works for more complex shapes, those with a dozen, even twenty or so rectangles and triangles, even with a semicircle thrown in. It's Maloney's assumption (and that of Pamela Martin, the previous author) that someone is asking for help in solving a middle-school geometry problem that is faulty. Maloney even blows that in her introduction:

"When you first start calculating area, you get easy shapes that have clearly defined formulas for finding their area: circles, triangles, squares and rectangles, for example. But what happens when you're faced with a shape that doesn't fit easily into those categories? Until you enter the brave new world of calculus integrals, the best way to find the area of irregular shapes is by subdividing them into shapes you're already familiar with."

Just what makes Lisa think that the question was about homework? Why couldn't the OQ have wanted to calculate the area of a city lot, or of a larger area? For instance, it looks pretty easy to calculate the area of the state of Colorado (a rectangle) or of Utah (a "fat" L), but what about Michigan? How do we know that the area of the state is 96,716 square miles (bigger than Utah, smaller than Colorado)?

We know because there is, in fact, a fairly simple method for calculating the area of a polygon of any number of sides, regardless of the angles between them. All it takes is knowing – or generating – a pair of x,y coordinates for each of the polygonal vertices. The advantage is obvious: you don't have to sit down with a piece of graph paper and attempt to divide a complex polygon into a list or simple polygons (some of which, to quote Maloney, will require  "the brave new world of calculus integrals" to solve.
For failing to even attempt to address the question of a polygon that cannot be expressed as a list of simple polygons despite her "several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus," Maloney wins the Dumbass of the Day, Rewrite Division, for the second time.

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