Calculating volume by area and thickness

Question

I have an irregular hexagon that is $1\,mm$ thick. The total area of the hexagon is $114.335\,cm^2$.

How do I calculate the volume?

Answer 1

Volume is in general Area times Depth. Just by knowing the area and thickness, you can multiply these together. Make sure you first convert your units to either mm or cm. 1mm = .1cm Your answer would then give you cm^3 (centimetres cubed) as units

Answer 2

A description like 'the total area is...' is quite amibiguous here.

Once a hexagon got a thickness it is no longer a polygon but rather a polyhedron (a hexagonal prism), and it has no just an area but rather a top area, a base area and a side area (where a side is a sum of six faces, corresponding to $6$ sides of a hexagon). Then 'a total area' usually means a sum of areas of all $8$ faces.

This interpretation, however, would render a problem unsolvable: if the base (the original hexagon) area is $B$, a total area is $A$, the perimeter of a hexagon is $p$ and the thickness is $h$, then $$V=Bh = \frac{A-ph}2h$$ Given $A$ and $h$ we can't calculate $p$, consequently can't determine $V$.