I can't imagine any way short of calculus that would be valid.
![calculator for volume of triangular prism calculator for volume of triangular prism](https://showme0-9071.kxcdn.com/files/151709/pictures/thumbs/790348/last_thumb1363608259.jpg)
My big question, before I go through my work again, is what this is doing as an 8th grade assignment. It's not too hard in principle, but my quick attempt just now gave a different answer than yours. I would certainly use calculus as you suggest.
#CALCULATOR FOR VOLUME OF TRIANGULAR PRISM TRIAL#
(And making a trial guess like that as a basis for checking a final answer, or even hoping it might be demonstrably optimal, is quite reasonable. (They might instead assume it's a right triangle, just to make some things simpler, but that's unlikely to be true.)Īssuming the height is also the same is reasonable as a first guess (given what we know about cubes), but far less justifiable. If this makes sense as an 8th grade problem at all, the assumption that it's equilateral is natural and probably necessary. If you were a student of multivariable calculus, I would expect you to prove everything. This is not to earn a mark for a course, but rather to satisfy my own curiosity. I have searched quite a bit to find an example of a similar question, but cannot seem to find one on the internet.
![calculator for volume of triangular prism calculator for volume of triangular prism](https://i.ytimg.com/vi/bxZ1ao0HEg4/hqdefault.jpg)
I am also fairly certain I need to apply some calculus and find a derivative somewhere along the line to solve it properly. (I believe the answer is very close to a volume of 5336 cubic centimetres. (Yes, a guess, but I did actually do the work to determine this.) Some quick trial and error have shown me that, while my answer isn't ridiculously far off, it is not the correct one. I solved and determined a side length of 22.74cm presuming an equilateral triangle and an equal height for the prism. I am aware that critical information is missing from the question, but that is all that was provided. I have seen the assignment page, but it is not currently with me.
![calculator for volume of triangular prism calculator for volume of triangular prism](https://og-imgs.omnicalculator.com/calculator/1366/Vm9sdW1lIG9mIGEgVHJpYW5ndWxhciBQcmlzbSBDYWxjdWxhdG9y.png)
There is literally no other information included in the question aside from the total surface area and the fact that it is to be a triangular prism. Honestly, this is a grade 8 question that was given to my niece and I (an intermediate math teacher) am trying to figure out the answer.