# What is the volume of a hexagonal prism where one end is bigger than the other

I had assumed that it would be the average of the top and bottom areas multiplied by the height, but this does not seem to give an accurate answer (about 1% over estimated). Is my google sketchup wrong, or my maths?

eg. suppose, top edge length is et= 6.25, bottom edge eb= 5, and height h=15. My formula  0.75*sqrt(3)*h*(et^2+eb^2)  gives 1248.29 whilst google gives 1238.15

See attached diagram showing the exploded object.

Thanks!
hexagonal-box.JPG
Asked:
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Commented:
I can't do the maths in my head with your values, but the formula for the volume of a cone with any shaped Base is one third of the Base area multiplied by the vertical height. If you calculate the full height of your object when extending the sides to a point you can calculate the volume of the full object and subtract the volume of what you added to extend it. An average of top and bottom times height doesn't sound wrong but I can't check at the moment. Hopefully the cone formula will give you another way to check the result.
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Commented:
Average of top and bottom times height does not work because you are in three dimensions.

The formula for a trapezoid area is average top and bottom times height because the formula for a triangle is 1/2 base*height (which is the same as average of top and bottom since top is 0 and bottom is base).

Since you have a 3D solid, you'll want to base your formula off a cone/pyramid (as suggested by Ors-Ankh-Aten). That will work well.

Of course, calculating the projected height is a pain. You can skip that because it is given by the ratio of the base to the height.

Here is the short-cut formula.
http://www.ditutor.com/solid_gometry/volume_truncated.html
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Author Commented:
Thanks guys, that is excellent and the result now works.
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