Volume of a Tetrahedrom

[Trenters4325]

How would you show that the volume of a tetrahedron is equal to 1/3(base)height?

 

[pka]

Have you tried the MathWorld website?
http://mathworld.wolfram.com/Tetrahedron.html

 

[Trenters4325]

I did not see it there.

 

[pka]

I did not see it there.

What do you mean?

Do you mean that the site did not give a complete solution?
Do you mean that you do not understand enough to use its information for a proof?
Do you mean that you are too lazy to do the work it takes to do a proof?

 

[Trenters4325]

The second statement would best describe what I mean. A lot of that site was over my head, and there so much information that I had no idea where to begin the proof.

 

[Denis]

How would you show that the volume of a tetrahedron is equal to 1/3(base)height?

What do you mean by (base) ?

 

[Trenters4325]

The base is the area of the triangle orthogonal to the height. Actually, its the same formula for any pyramid, so I just need a proof for pyramidal case.

 

[Denis]

Right; usually shown as Ah/3 where A = area of base.

You'll find lots of sites using a google search on "proof volume of pyramid";
here's a good one:

http://mathschallenge.net/index.php?sec ... me_pyramid