Bases and FacesDate: 12/05/2001 at 14:07:24 From: Madison Subject: Bases and faces In math class we are learning about polygons and I can't figure out the difference between a base and a face on the shapes we are learning. My teacher says a face is a base but a base is not a face. What is the difference? How many bases does a cube have, and how many faces does it have? Date: 12/05/2001 at 14:48:31 From: Doctor Peterson Subject: Re: Bases and faces Hi, Madison. We generally use these terms in different settings. A cube on its own has six faces. Here we're not picturing it set on a table, but just sort of floating in space, so that all six faces are equal, and we don't think of any of them as special. When we are talking about how to calculate the area or volume, we usually think of one face as the "bottom," and call it the base, as if we were setting it down on a table to measure it. The "top" may be seen as "the other base," since they are identical, and the other faces are the "sides." So when you set the cube down, it has one base (or two if you prefer) and four sides. It really doesn't make any difference which face you call the base when you talk about a cube, because they are all the same. But for, say, a box (a rectangular parallelepiped), you have three different lengths, and by choosing a base you are deciding which two lengths to use to find the area of the base, and which length to call the height. You can choose any face to be the base, and you will get the same answers. For some shapes, such as a cone, there is only one flat surface to use as the base. Then no questions arise (until you ask whether the curved "side" can be called a face - but that's another question, and we've answered that in our archives). Incidentally, I am assuming you are learning about polyhedra, not polygons; the latter are flat. A cube is a polyhedron. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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