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Volume of a tetraedron in function of the areas

  1. Jun 15, 2015 #1
    Given any tetraedron, I want to calculate the volume V in function of the areas of the surfaces of the solid. I found this pdf that explain this:

    http://daylateanddollarshort.com/mathdocs/Heron-like-Results-for-Tetrahedral-Volume.pdf

    But, o pdf says that beyond of the 4 faces (X, Y, Z, W) is necessary more 3 pseudo-faces (H, J, K). But, is it correct? Is really necessary 7 areas for compute the volume? With just 4 is not possible?
     
  2. jcsd
  3. Jun 15, 2015 #2

    Simon Bridge

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    Have you tried working it out for the areas of 4 faces alone?

    The trouble is that the area of a triangle does not determine it's shape - so you can construct many differently volumed tetrahedra out of four triangles knowing only their areas (but not their shapes).
     
    Last edited: Jun 15, 2015
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