بعد الاجتماع سألت الاستاذة عن سبب القرار.

بعد means after, but in Arabic it behaves like a noun/adverb of time rather than an English-style preposition.

So بعد الاجتماع literally works like after the meeting.
Grammatically, بعد is followed by a noun in an iḍāfa construction, so الاجتماع is in the genitive:

بعدَ الاجتماعِ

You do not add another preposition here.

Because normal Arabic writing usually leaves out short vowels.

So سألت can represent several different forms, such as:

• سألتُ = I asked
• سألتَ = you (masc. singular) asked
• سألتِ = you (fem. singular) asked
• سألتْ = she asked

The intended meaning is usually clear from context, case endings, or the translation shown to the learner.

The case ending tells you:

• الأستاذةُ = nominative, so it is the subject
• الأستاذةَ = accusative, so it is the direct object

So these are different:

• سألتْ الأستاذةُ عن سبب القرار = The female teacher asked about the reason for the decision
• سألتُ الأستاذةَ عن سبب القرار = I asked the female teacher about the reason for the decision

Without vowel marks, both look very similar in writing.

With سأل, Arabic often uses:

• the person asked as a direct object
• the topic asked about with عن

So:

سألتُ الأستاذةَ عن سبب القرار
= I asked the female teacher about the reason for the decision

This is a very common pattern:

• سألتُه عن الموضوع = I asked him about the topic
• سألوا عن الأسعار = They asked about the prices

This is an iḍāfa construction:

• سبب = reason
• القرار = the decision

So literally it is reason of the decision, which English naturally translates as the reason for the decision.

Arabic often uses iḍāfa where English uses of or for.

In an iḍāfa construction, the first noun usually does not take ال.

So Arabic says:

• سبب القرار

not:

• السبب القرار

Even though سبب has no ال, the whole phrase is definite because the second noun is definite. So سبب القرار means the reason of the decision, not just a reason of a decision.

الأستاذة is the feminine form of أستاذ.

It can mean:

• the female teacher
• the female instructor
• the female lecturer
• sometimes the female professor

The exact English choice depends on context. The ending ة is the common feminine marker.

In careful Modern Standard Arabic, the standard spelling is:

الأستاذة

with a hamza on the alif.

Writing الاستاذة without the hamza is common in informal typing, but it is not the most careful standard spelling.

Yes. Arabic is flexible with word order, especially for time expressions.

For example:

• بعد الاجتماع سألتُ الأستاذةَ عن سبب القرار
• سألتُ الأستاذةَ عن سبب القرار بعد الاجتماع

Both are possible. Putting بعد الاجتماع first gives the time setting immediately: After the meeting...

If the intended meaning is I asked the female teacher about the reason for the decision, the fully vowelled form is:

بعدَ الاجتماعِ سألتُ الأستاذةَ عن سببِ القرارِ

If the intended meaning is The female teacher asked about the reason for the decision, it would be:

بعدَ الاجتماعِ سألتْ الأستاذةُ عن سببِ القرارِ

In normal everyday Arabic writing, these short vowels are usually omitted, which is why the written sentence can look ambiguous.