kono chiiki wa shizuka desu.

この means “this” and is used before a noun to indicate something close to the speaker.

• その means “that” (near the listener).
• あの means “that over there” (far from both speaker and listener).

地域 (ちいき) is a Sino-Japanese noun meaning “area” or “region,” often with a slightly formal or administrative nuance.

• 場所 (ばしょ) is a more general word for “place” (anywhere you can go).
• エリア is an English loanword (area) used in casual speech, advertising, etc.

は marks the topic of the sentence (“As for this area”). It sets what you’re talking about.

• が marks the subject or introduces new information/emphasis (“It is this very area that is quiet”).
  In most descriptive sentences about a known topic, は is the natural choice.

静か (しずか) is a な-adjective (also called an adjectival noun).

• To use it with the copula, you simply add です (→ 静かです).
• If you used に (静かに), you’d turn it into an adverb meaning “quietly.”

です is the polite copula “to be.” It makes your statement polite.

• In casual (plain) speech you replace です with だ:
  この地域は静かだ。

Start with 静か + the polite copula endings:

• Negative present: この地域は静かではありません or 静かじゃありません.
• Past affirmative: この地域は静かでした.
• Past negative: この地域は静かではありませんでした.

In English, quiet can behave like a verb (“The room quiets down”). Japanese prefers describing states with adjectives or adjectival nouns plus the copula:

• 静かです = “(It) is quiet.”
  Verbs meaning “become quiet” exist (e.g. 静まる), but for simple descriptions you use 静かです.