Wow! That is so amazing.
So I hypothesise that it's built like this:
pre + post + erous --> preposterous
And it means "before" "behind" - kind of like 'topsy-turvy' or 'putting the cart before the horse'. How cool is that?
I'm not sure about the exact word sum yet - as maybe the base is <poster> or even <posterous>, but I do know that <er> is a suffix, and <ous> is a suffix, so my hypothesis is at least 'possibly' correct. I know that <post> means "after" in words such as <post-natal> ("after" "birth") and <post-mortem> ("after" "death"). And then there's post-modern, post-graduate, postscript (i.e. P.S. at the end of a letter), and of course posterity "coming after" and posterior.
I will leave it there - but with kids (and adults) who are new to this way of looking at spelling, I'd point out that the <pre-> just joins on to the base without any changes being necessary. This is because prefixes are boring - they just join on. This is another tidbit of learning that can be applied to hundreds/thousands or words, and can be taught through this one investigation of an interesting word encountered in a reading book.
Sorry I called you boring, prefixes, but it's true. All you do is hook on without causing any changes. You must be so jealous of those suffixes that start with vowels. They can change the last letter of the base, whereas you can't do anything to the base. Why do they get to have all the fun?