Away is definitely not an adjective because you will never say
"*The away man" or some other such thing.
It also can't be an adverb modifying the verb in this example because adverbs don't come after "to be"
"*The building is greatly"
SO it is either a preposition or an adverb modifying a prepositional phrase, I don't have the time to completely figure it out but I'll leave my data for everyone else to work with.
I'm going to modify your examples so they're more similar if that's alright with you:
"The building is ten feet tall"
"The building is ten feet away"
Let's see what we can do here.
"The ten feet tall building is brown"
"*The ten feet away building is brown"
"*The building ten feet tall is brown"
"The building ten feet away is brown"
Weird! Seems like "away" and "tall" behave differently in different contexts. WHAT ELSE?!
"The building is ten feet into the alley"
"*The ten feet into the alley building is brown"
"The building ten feet into the alley is brown"
Now we're onto something!
"There is a building ten feet into the alley"
"There is a building ten feet away (from right here)"
"*There is a building ten feet tall"
It would appear that in this usage, "away" is an abbreviation of "away from (something)". Furthermore, it seems that when you don't say "from X", the X is automatically defined as "the origin of the speaker" whereas:
"There is a building five minutes away from my office"
"There is a building ten feet away from the mall"
Without the parenthesis, "from right here" is the implication.
Now that's all pretty soft evidence. But now check this out:
"The shop is ten feet away (from the store)"
"The shop is ten feet past the store"
"*The shop is ten feet past"
While 'away' implies the rest of the prepositional phrase and so does not require it, 'past' does not, yet functions the same:
"The shop ten feet past my house"
"There is a shop ten feet past my house"
"*The ten feet past my house shop"
Past is certainly a preposition:
"I walk past the store every day"
But of course, "away" precedes a preposition. Prepositions sometimes come two in a row, but rarely. It can precede other prepositions as well:
"I wanted to get away with it"
"I went away to the Bahamas"
In fact, I can't think of a single instance in which "away" exists entirely by itself without implying another prepositional phrase!
HOWEVER I also can't think of any other adverbs that modify prepositions.
(EDIT: This is clearly super wrong! Really eatin my apples for this one. I hope I get a chance to come back and rethink it.)
SO in conclusion, away is a very complicated potentially preposition.
Hope that helps!