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Three Sided Pyramid Volume Question.

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For the record I'm 56, so this isn't homework. :)

I've enclosed a diagram of the problem I'm working for reference. 

Start with a cube. All edges are the same value. For reference, the corners of the cube are designated by numbers, the middle point of each edge is identified by a letter. Clear as mud? 

I need to take away the corners and determine the volume without them. One corner is determined by lines from A -> D  D -> F  F -> A

Assuming each edge is 3.720, the middle point (from 1 -> D or D -> 4) is 1.860.

Finding the distance from A -> D is found by simple trig to be 2.63044

The volume of a three sided pyramid can be found with the formula V = 1/3AH 
A = area of the triangle base. H = height of the pyramid.

I know A = 2.99611, but how do I find H or the height in that scenario? Once I know that I can multiply corner volume by 8 to get the volume of all eight corners and subtract it from the whole. 

Thanks.

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Three Sided Pyramid Volume Question. Simon <shadragon@excite.com> - 2017-11-08 19:44 +0000

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