Area and Perimeter for Mathematical Dummies

Regular polygons

The research staff at the Antisocial Network have noticed that some of the freelance writers searching for pennies aren't particularly... perhaps we should say "intellectually honest." Well, it's either that or they're total dumbasses: we're not certain which is more likely. Today we're thinking, in particular, of the stable of contributors to eHow.com; many of whom have no objection to telling someone how to do something that's impossible or expanding a bad answer from one word to 500 in order to collect their ten or fifteen bucks. And then there are the ones who provide half-assed "answers."Take, for instance, Charlotte Johnson: Char's a typical eHowian, meaning someone who happily writes about STEM topics even though s/he lacks any pertinent background. Let's have a look at a Johnson post, one that purports to explain "How to Calculate Square Feet From the Perimeter"¹ at niche site Sciencing.com.

Charlotte, required by eHow to open her content with some form of introduction, "explains" that

"Square feet is a term that applies to the measurement of the area of a shape. The perimeter of a shape is the length of the outer border of a shape. You can calculate the area of a figure when given the perimeter if that figure is a square or a circle."

Johnson's answer is the sort of narrow thinking that permeates eHow.com. Rather than explaining that you can calculate the area of any regular polygon from the perimeter if you are willing to perform the necessary geometric, algebraic and trigonometric calisthenics; Charlotte simply says you can calculate the area of a square or circle. What's more important is that Johnson never bothers to mention that, unless 1) the polygon is regular and 2) you know the number of sides, deriving area from perimeter is impossible (unless you know the Cartesian coordinates of all the vertices). For instance, here is the sequence of steps needed to calculate the area of a "regular" (i.e., equilateral) triangle with a perimeter of 24 units: calculate the base, or length of one side: b = 24 / 3 = 8 calculate the height using the Pythagorean theorem: h = ((8/2)^2 + 8^2)^0.5 = 80^0.5 = 8.94 calculate area: A = (b*h)/2 = 35.8 units²

Yes, given the formula for area, a scientific calculator and some general knowledge, you can calculate the area of any regular polygon; but not an irregular polygon. In fact, if you're really, really smart (not an ordinary eHowian, in other words) you'd look up the general formula for calculating area from perimeter of a regular polygon: yes, there is one. In fact, there are three!

Some version of that should have been Johnson's answer, but she was too lazy or, more likely, too dumb to look it up. Darned shame for her, but great for the Antisocial Network because we get to hand out yet another Dumbass of the Day award.

¹ Leaf called in one of their "specialists" to rewrite Charlotte's dumbassery, one Lisa Maloney. It appears that Lisa's vast experience as a personal trainer and travel writer were not equal to the task, however, since her version is just as stupid as what Johnson wrote...

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