الطابق الأرضي مزعج.

Because in Arabic, the verb to be is usually not written or spoken in the present tense.

So:

الطابق الأرضي مزعج.

literally looks like:

the ground floor annoying/disturbing

but it means:

The ground floor is annoying / noisy.

This is a very normal Arabic sentence pattern, called a nominal sentence. In the present tense, Arabic simply puts the subject and predicate next to each other.

If you wanted the past, you would add كان:

كان الطابق الأرضي مزعجًا
The ground floor was annoying.

Because الأرضي is an adjective describing الطابق.

In Arabic, adjectives usually match the noun they describe in:

• definiteness
• gender
• number
• case

So if the noun is definite, the adjective must also be definite.

Here:

• الطابق = the floor/story
• الأرضي = ground / ground-level

So:

الطابق الأرضي = the ground floor

This is different from English, where ground floor looks like a noun + noun combination. In Arabic, it is more naturally understood as noun + adjective.

No, it is not an iḍāfa.

It is a noun + adjective phrase.

Why not iḍāfa?

• In an iḍāfa, the first noun usually does not take الـ if it is definite through the second noun.
• The second word in an iḍāfa is a noun, not an adjective.
• Here, الأرضي behaves like an adjective and agrees with الطابق.

So this is:

• الطابق = noun
• الأرضي = adjective

not:

• noun + possessed noun

A learner often wonders this because English sometimes uses noun combinations where Arabic uses adjectives.

Because مزعج is the predicate of the sentence, not an adjective inside the noun phrase.

The structure is:

• الطابق الأرضي = the subject
• مزعج = the predicate

In Arabic nominal sentences, the predicate is often indefinite, so it usually does not take الـ.

So:

الطابق الأرضي مزعج
= The ground floor is annoying / noisy

If you made مزعج definite, the meaning would change or sound much less natural in this simple sentence.

This is a nominal sentence:

• الطابق الأرضي = mubtadaʾ (the topic/subject)
• مزعج = khabar (the comment/predicate)

More specifically:

• الطابق is the head noun
• الأرضي is an adjective modifying it
• مزعج is an adjectival predicate

So the sentence says something about the ground floor: namely, that it is annoying / noisy / disturbing.

Yes. الأرضي is masculine because الطابق is masculine.

Arabic adjectives agree with the noun they describe. So if the noun were feminine, the adjective would usually become أرضية.

For example:

• الشقة الأرضية = the ground-floor apartment
• القاعة الأرضية = the ground-floor hall

Likewise, the predicate would also agree in gender:

• الشقة الأرضية مزعجة = The ground-floor apartment is annoying/noisy

So in your sentence:

• الطابق = masculine
• الأرضي = masculine
• مزعج = masculine

With full case endings, it would be:

الطابقُ الأرضيُّ مُزعِجٌ

In careful grammar:

• الطابقُ is nominative because it is the mubtadaʾ
• الأرضيُّ matches it, so it is also nominative
• مزعِجٌ is nominative because it is the khabar

In normal everyday writing, these endings are usually not written, so you normally see:

الطابق الأرضي مزعج

A learner should know the endings exist, even though most Arabic text leaves them out.

In الطابق, the l of الـ is not pronounced, because ط is a sun letter.

So الطابق is pronounced approximately:

aṭ-ṭābiq

not:

al-ṭābiq

But in الأرضي, the l of الـ is pronounced, because the word begins with hamza, which is a moon letter.

So:

• الطابق → aṭ-ṭābiq
• الأرضي → al-ʾarḍiyy
• مزعج → muzʿij

A careful paused pronunciation of the whole sentence is roughly:

aṭ-ṭābiq al-ʾarḍiyy muzʿij

Its basic sense is closer to annoying, disturbing, or bothersome.

Depending on context, it can be translated more naturally as:

• annoying
• disturbing
• noisy
• a nuisance

So if the idea is that the ground floor has a lot of sound, traffic, or disruption, English might translate it as noisy even though مزعج is a bit broader than that.

A more specifically “noisy” word would often be something like:

• صاخب = noisy / loud

But مزعج is very common when something causes annoyance.

You generally would not use that as the neutral basic word order.

The normal order is:

الطابق الأرضي مزعج

That is the straightforward sentence: The ground floor is annoying.

Arabic can sometimes put the predicate first for emphasis or stylistic reasons, but that is not the default pattern learners should start with.

So for normal MSA usage, keep:

subject first + predicate second

Yes, in many contexts you may hear or see الدور الأرضي for ground floor.

However, for standard-learning purposes:

• طابق commonly means floor/story of a building
• الطابق الأرضي is a very clear and standard expression

Different regions may prefer one expression over another, and some forms are more common in everyday speech than in formal writing. But الطابق الأرضي is perfectly good MSA.