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### Pyramids and Triangular Prisms

```
Date: 05/09/2000 at 16:14:56
From: Victoria
Subject: Math Help

Dear Dr. Math,

I need help finding shapes of triangular prisms. I get pyramids and
triangular prisms mixed up. What's the difference between them?
```

```
Date: 05/09/2000 at 21:09:34
From: Doctor Peterson
Subject: Re: Math Help

Hi, Victoria.

One of the things that make math more pleasant is seeing what the
words are all about. So let's look at what a prism and a pyramid are.

In either case, you start with some plane figure - a triangle, a
square, or whatever. To make a prism, just make a second copy and move
it somewhere outside the plane, keeping it parallel - that is, just
slide it straight up. (If you slide it vertically, so it's exactly
over the base, we call it a "right prism," meaning it goes up at right
angles to the base. If you slide it up at an angle, it's an "oblique
prism.")

Say you've drawn a triangle on your desk. Put an identical triangle on
top of it and lift the second triangle straight up above the desk. Now
imagine connecting each vertex of the bottom triangle to the
corresponding vertex of the top triangle. You've just made a right
triangular prism:

+
/   :\
/       : \
+--------------+
|           :  |
|           +  |
|       .    . |
|   .         .|
+--------------+

The volume of a prism is just the product of the area of the base and
its height; think of it as a stack of pancakes whose volume is the
product of the size of each pancake and the number of pancakes.

To make a pyramid, you start with a base as before. But this time,
instead of putting a copy of the base above it, just make a single
point somewhere up in the air, and connect every vertex of the base to
that one point:

+
/ |\
/   |\
/     + \
/   .    .\
/ .         .\
+--------------+

The volume of a pyramid is obviously less than a prism of the same
height; it's a stack of pancakes that get smaller and smaller as you
go up. It turns out that it's exactly 1/3 the volume of the prism.

For pictures of prisms and pyramids, see the Dr. Math FAQ:

Prism Formulas
http://mathforum.org/dr.math/faq/formulas/faq.prism.html

Pyramid and Frustum Formulas
http://mathforum.org/dr.math/faq/formulas/faq.pyramid.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Geometry
High School Higher-Dimensional Geometry
High School Polyhedra
Middle School Definitions
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Polyhedra

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