Associated Topics || Dr. Math Home || Search Dr. Math

### Bases and Faces

```
Date: 12/05/2001 at 14:07:24
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

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

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

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/
```
Associated Topics:
Elementary Geometry
Elementary Polyhedra
Elementary Three-Dimensional Geometry
High School Geometry
High School Higher-Dimensional Geometry
High School Polyhedra
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Polyhedra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search