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Volume of a weird shape


Hello all!

I was in practicing BIM (building information modeling) at school when our teacher told us than crazy shapes aren't an issue anymore when it comes to determinating a volume since we can rely on computers. We now just have to draw it in 3D and softwares can give us the answer we need.

I was curious about how it was done before all that. Here's an example : From above, a rectangular shape. Corners at the same higher height are merging into a point at a lowest height. See attached picture. I tried to figure the volume by hand considering a whole rectangular parallelepiped from which I substracted parts of rectangular based pyramids. Well, turns out I can't manage do find the good answer.

Can anyone? I doubt it will bother you as much as it did bother me.


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