Der Saum am Hosenbein ist zu lang.

Because Saum is a masculine noun in German: der Saum.

In this sentence, Der Saum is the subject, so it is in the nominative case, and the correct article is der.

A useful thing to memorize is:

• der Saum = the hem
• den Saum = the hem (object)
• dem Saum = to/from/on the hem

Saum means hem: the folded and sewn edge of a piece of clothing.

In this sentence, it refers to the hem of the trouser leg, not to the whole pair of trousers.

So:

• der Saum = the hem
• das Hosenbein = the trouser leg / pant leg

Because am is the normal contraction of an dem.

So:

• an dem Hosenbein → am Hosenbein

This contraction is very common in German, just like:

• im = in dem
• vom = von dem
• zum = zu dem

In this sentence, am Hosenbein means on the trouser leg.

Because it follows the preposition an, and here an describes a location, not movement.

German two-way prepositions like an can take:

• accusative for movement toward something
• dative for location

Here, the hem is located on the trouser leg, so German uses the dative:

• an dem Hosenbein → am Hosenbein

Compare:

• Der Saum ist am Hosenbein. = The hem is on the trouser leg.
• Ich nähe den Saum ans Hosenbein. = I sew the hem onto the trouser leg.

Because Bein by itself usually means leg in the body-part sense.

If you want to talk about the leg of a pair of trousers, German often uses the compound noun Hosenbein:

• Hose = trousers / pants
• Bein = leg
• Hosenbein = trouser leg / pant leg

This is very natural German.

Also notice that in compounds, the last part decides the gender:

• das Bein
• therefore das Hosenbein

Yes, the basic noun is die Hose. In the compound Hosenbein, the first part appears as Hosen-, which is a common linking form in German compounds.

You do not need to treat it as a separate plural here. Just learn Hosenbein as the normal word for trouser leg / pant leg.

This kind of thing is very common in compounds:

• Hose → Hosenbein
• Arbeit → Arbeitszimmer
• Kind → Kindergarten

So the -n- is part of the compound form.

Because lang is a predicate adjective here: it comes after ist.

After verbs like sein, werden, and bleiben, adjectives usually do not take endings:

• Der Saum ist lang.
• Die Ärmel sind kurz.
• Das Kleid ist schön.

But when an adjective comes before a noun, it does take an ending:

• der lange Saum
• die kurze Hose
• das schöne Kleid

So:

• der Saum = noun phrase
• ist zu lang = predicate adjective phrase

No. Here zu means too, not to.

So:

• lang = long
• zu lang = too long

It expresses that something is longer than desired or appropriate.

Compare:

• Der Saum ist lang. = The hem is long.
• Der Saum ist sehr lang. = The hem is very long.
• Der Saum ist zu lang. = The hem is too long.

That last one suggests a problem: it should probably be shortened.

German works differently from English here.

English often uses:

• pants
• trousers

German usually uses the singular noun:

• die Hose = pants / trousers

And when talking about one leg of the garment, German uses the singular:

• das Hosenbein = the trouser leg / pant leg

So am Hosenbein refers to one specific trouser leg, which makes perfect sense in German.

Yes, you could, and it is grammatically correct.

• Der Saum am Hosenbein ist zu lang.
• Der Saum des Hosenbeins ist zu lang.

The first version sounds more everyday and spatial: the hem on the trouser leg.
The second uses the genitive: the hem of the trouser leg.

Both are possible, but am Hosenbein is very natural in ordinary speech.

No, it is quite standard.

The sentence structure is:

• Der Saum = subject
• am Hosenbein = prepositional phrase
• ist = verb
• zu lang = complement

So the full sentence is: Der Saum am Hosenbein ist zu lang.

German often places descriptive information like am Hosenbein right after the noun it belongs to, which makes the sentence easy to understand.

A rough English-friendly guide:

• Saum ≈ zowm
  The au sounds like the ow in cow.

• Hosenbein ≈ HOH-zen-bine
  The ei sounds like English eye.

A few details:

• German s at the start of Saum is pronounced like z
• Hosenbein has stress on the first syllable: HO-zen-bein

So the sentence sounds roughly like: Dare zowm am HOH-zen-bine ist tsoo lang

That is only approximate, but it helps as a starting point.