Learn Hardcore German: Die Innenstadt ist so voll wie der Bereich am Rand des Parks. - The city center is as crowded as the area at the edge of the park.

Use so + adjective + wie for equality: it says two things have the same degree of a property (here: being crowded/full).
Use als only with a comparative form (e.g., voller als, mehr … als).
Natural variants for equality are genauso voll wie and ebenso voll wie.
Regional (mainly AT/CH): gleich (so) voll wie is common; in formal Standard German, prefer (genau)so … wie.

Why is it der Bereich and not den Bereich or dem Bereich after wie?

After wie, you use the case required by the clause that is implicitly omitted. Expanded, it’s “Die Innenstadt ist so voll, wie der Bereich am Rand des Parks (ist).” In that clause, der Bereich is the subject, so nominative der, not accusative den or dative dem.

Compare:
- Equality with subject: Er ist so groß wie ich (not “wie mich”).
- Equality with object: Sie mag ihn so sehr wie mich (here “mich” is correct because the verb “mag” would take accusative in the implicit clause).

What is am in am Rand, and why is it dative?

am = an dem (contraction).
an is a two-way preposition:
- Dative for location (no movement): am Rand = “at the edge.”
- Accusative for movement toward: an den Rand = “to the edge.”

Why is it des Parks? Can I say vom Park instead?

des Parks is the genitive, expressing “the edge of the park.”
am Rand vom Park (dative with von) is common in everyday speech and perfectly understandable; in formal writing, genitive (des Parks) is preferred.
Older/poetic genitive des Parkes also exists but is rare today.

Do I really need der Bereich? Could I say something shorter?

Acceptable and idiomatic: Die Innenstadt ist so voll wie am Rand des Parks. (Ellipsis of “es [ist] …”: “as crowded as [it is] at the edge of the park.”)
Possible but a bit odd: … so voll wie der Rand des Parks. People usually avoid calling a “line/edge” itself “full”; they mean the area there. More natural: … wie die Gegend am Rand des Parks or … wie der Parkrand.
Keeping der Bereich makes it explicit you mean an area/zone, not a literal border line.

Why do we need the article in Die Innenstadt? In English I’d say “Downtown is …” without “the.”

German normally uses an article with singular countable nouns, even for unique places like die Innenstadt, die Schule, die Universität. Dropping the article is common only in headlines, signs, or certain set phrases.

Is voll the best word here? What about überfüllt or others?

voll is standard and common for places: “full/crowded.” Neutral in tone.
überfüllt = “overcrowded,” stronger/negative.
belebt = “lively/busy,” positive and less about discomfort.
Colloquial intensifiers: rappelvoll, proppenvoll (very crowded).
Note: voll sein can colloquially mean “to be drunk,” but context (a place) prevents confusion.

Why doesn’t voll take an ending here?

Because it’s a predicate adjective after sein. Predicate adjectives in German are not inflected:

Die Innenstadt ist voll.
Attributive adjectives before a noun do inflect: die volle Innenstadt, der volle Bereich.

Is am Rande des Parks also correct?

Yes. am Rande is a slightly more formal/literary variant of am Rand. Both are correct; am Rand is more neutral and common in everyday speech.

Any pronunciation tips for tricky parts?

Innenstadt: stress on the first syllable; the St in Stadt is pronounced like “sht” in Standard German (because it begins the second part of the compound).
Bereich: be-REICH (like “rye” at the end), with the soft ch as in ich.
Rand: rolled/uvular German R; short “a.”
Parks: pronounce the final -s as “s,” not “z.”
wie: “vee” (long i).

What genders and cases are in play here?

Die Innenstadt: nominative singular feminine (subject).
ist: 3rd person singular of “sein.”
so voll: predicate adjective (no ending).
wie: comparative conjunction for equality.
der Bereich: nominative singular masculine (subject of the implied clause after wie).
am Rand: dative singular masculine (contraction of an dem Rand) because it’s a location.
des Parks: genitive singular masculine, dependent on Rand (“edge of the park”).

Could I add a verb after wie, e.g., …, wie der Bereich am Rand des Parks ist?

Grammatically possible but stylistically clunky. In equality comparisons, German overwhelmingly prefers the ellipsis:

Natural: … so voll wie der Bereich am Rand des Parks.
If you really expand it, a comma is needed: … so voll, wie der Bereich am Rand des Parks ist. Most natives would avoid this fuller version.