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I have the following shape

I want to calculate the volume of this shape, it's basically a frustum with an irregular polygon base. The bottom area $A_1$, the height of the frustum shape $h$,the sideways distance between $A_1$ and top area $A_2$ $ = s $ are known.Top area $A_2$ is unknown.

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2 Answers 2

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$$ Vol= (A1 + A2 + \sqrt {A1\cdot A2} )* h/3, $$

the relation assumes similar top and bottom polygonal shapes and concurrency of slant generators. Does not depend on side distance..

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  • $\begingroup$ The top area A2 i unkown, how would I calculate that from the given facts? $\endgroup$
    – JohnDev
    Apr 23, 2016 at 12:29
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Hint: If you treat the frustrum as a pyramid with the top cut off, then clearly the top face is similar to the bottom face, and the ratio of their dimensions is simply the ratio of the heights of the two pyramids (the small one cut off from the big one).

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