Pyramids and Triangular PrismsDate: 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/ |
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