What level is the water?

[Lepista]

Friday puzzle:

There are four defined points, forming a box. The sides might not be parallel. You have the (x,y) coordinates for each corner.

The box is (x%) full.

At what level is the water (what is the 'y' position)?

Solve via excel without using macros or dynamic formulae.

 

[Joe4]

Is this some sort of assignment or homework?

I would recommend finding the mathematical solution first, then apply it to Excel.

 

[Lepista]

Nope, I've done a very inelegant solution, I'd just like to see if there is a better way to do this on Excel.

With a triangle, the solution is relatively simple, however for a quadrilateral it appears to get very awkward indeed.

I found it fun to do, I thought it would be an interesting enough puzzle for others to try.

 

[Joe4]

If you could post the mathematical explanation/formulas on how to calculate it, someone may be able to help you apply it to Excel.

 

[Lepista]

I have already applied it to excel, but it's very messy. I don't want to prejudice other people thoughts about how to go about it by posting my (very poor) solution just yet, when there might be a different way to do so.

 

[Joe4]

OK, I am going to move this thread to the "General Discussion & Other Applications" forum, as it is probably more of a math question than Excel one (at least, that is the hard part).
Once a good mathematical formula is determined, translating it to Excel shouldn't be difficult.

 

[Lepista]

It's definitely not a maths problem - It's an excel issue. Ther is no "formula" for it - it's definitely about manipulation in excel.

My spoiler: My answer revolves around arranging the four corners in height order, with the caveat that there's an issue if coordinates are the same height (y coord) or the same x position.

 

[Joe4]

I disagree. Programming (in any langauge) is not magic, it is is very literal and can only do what you tell it to.
You cannot build a house without a plan (a blue print).

There is no way someone with an extensive knowledge of Excel, but none of math (mainly, trigonometry) would be able to figure this out.
You have to know what you are doing, have a "plan" in the trigonometry sense, before you can even begin to do anything in Excel regarding it.

 

[Lepista]

I agree, but the issue I had was not the maths ... OK, I'm going to give some more spoilers here, so look away if you want to play yourself:

The solution boiled down to (1) getting the coordinates arranged (just using excel "basic" formulae) from low to high, then finding the corresponding point on opposite point of the shape, then splitting the shape up into two triangles and a (simple) quadrilateral in between.

Issues I had to deal with were:
- If two points were the same height
- if the "opposite" side of the shape from the two points was on the same opposite edge

 

[Joe4]

OK, it wasn't quite clear if this was a Challenge that you already solved, and just wanted to see if others could,
or if you were just looking for a better way of doing it (in which case it might be helpful to post your solution).

The fact that you have not posted your solution leads me to believe it is a Challenge to others.
It will be interesting to see if anyone comes up with anything.
I was a math major in college, but that was a very long time ago, and I am afraid my trig skills have gotten too rusty to hazard a guess myself.