"هٰذِهِ الْبِناية جَديدة وَواسِعة."
Translation:This building is new and spacious.
It depends on what you are trying to tell.
The sentence you've mentioned actually presumes that the receiver (listener) KNOWS about this building and you are telling him or her that THIS IS IT.
But in the sentence above, the speaker is telling information about the building itself that it is new and spacious. In other words, the speaker is identifying the building (the building was not known before that). I'm sure the logic works the same in English as well as in Arabic.
"the is the new and spacious building"? Hmm, well, I'll take that as a typo. I guess you meant (this is the new and spacious building).
For comparison, I'll list some versions of this sentence and I hope it would be easier that way to compare and see the differences:
This building is new and spacious: هذه البناية جديدة وواسعة.
This is the new and spacious building: هذه هي البناية الجديدة والواسعة.
This is a new and a spacious building: هذه بناية جديدة وواسعة.
Notice the changes in the presence of the definite article (AL) to البناية (the building) and notice how the adjectives change accordingly. One point to consider: In English sentences, whatever comes before (is) is the subject, and whatever comes after (is) is the predicate. Projecting that into Arabic, it is useful to know that in such sentences (nominal sentences which start with nouns and can be complete without a verb), the subject is (as a standard) defined with AL. The predicate in such sentences in Arabic, is typically and as a standard, NOT defined. For this reason, when I see an adjective following a noun and both are defined, then I know that such adjectives are not predicates (telling information) but they are attributes (describing the noun). Attributive adjectives in Arabic come after the noun and mimic its status (gender, number and definition).
One more point worth mentioning about (2) here. This sentence do have some emphatic sense to it, and in such instances in Arabic, after (this) هذه the pronoun (with respect to gender of course) is added for added emphasis. For this reason, it is mentioned here هذه هي البناية (literally: this/she/the building). Some books teaching Arabic as far as I know, do equate the addition of هي or هو with (is) in English. But this is a wrong conception but probably they are trying to deliver the idea across and close as much as possible to the learner because most European languages do use the verb (to be) in forming sentences, while Arabic does not do that (like Russian in fact), except in the past and the future. Otherwise, it is possible for nominal sentences to be completed without any verbs at all, like the sentence above. Hope this clears some.