oh maths genii, please! again ... a volume-of-prism/formula question

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You have a hexagonal prism (prism here meaning a solid with a consistent cross-section, so imagine a hexagonal pillar).

The "surface area" [says the question; we'll come back to that: see * below] is 100 cm squared; the total volume is 3000 cm cubed. (The question is: what depth is your prism?)

Now, if by "surface area" the qu. means just one (six-sided, top or bottom) face of the hexagon, then the answer is easy.

But - and this is the * - could the question be referring to total surface area? Ie, is the information above (100 cm squared for surface & 3000 cm cubed for volume) enough to work out the actual dimensions (or a set of actual dimensions) for a hexagonal prism?

You helped AMAZINGLY before, with a formula for the surface area of a cuboid - so can you help with this one? Many fulsome thanks.

lol at teacher not understanding the answer

MMJ - your DH is a mathemagician

V=area of base x height

3000cm cubed = 100cm squared x height

height = 3000/100 =30cm

I am still a bit stuck on how the formula for the area of a regular hexagon is 3x^2.

However, ds confirms your dh's formula for that is correct ("because, mum, it's six triangles, not six squares"

you might like this to calculate areas

I found a really good book that answers questions like this

it's called Match Wits with the Kids

Thank you everybody! - and the book looks fantastic. I found one once (aimed at teachers) which was called Getting the Buggers to Think, but was kind of re the title.

Anyway, it seems that the question was meant to be the simple one, so my brain is now having a rest.

I do love Mumsnet - where else could you have an exchange like this?