Картонная коробка лежит на полу.

Because картонная is an adjective modifying коробка, and Russian adjectives must agree with the noun in gender, number, and case.

Here, коробка is:

• feminine
• singular
• nominative

So the adjective also has to be feminine singular nominative: картонная.

Compare:

• картонная коробка = a cardboard box
• картонный ящик = a cardboard crate/box, with ящик being masculine

Коробка is in the nominative case because it is the subject of the sentence — the thing that is doing the action of лежит.

In English, we do not usually see this change clearly, but in Russian the subject normally appears in the nominative.

Compare:

• Коробка лежит на полу. = the box is lying on the floor
• Я вижу коробку. = I see the box

In the second sentence, коробку is a direct object, so it changes case.

Лежит is the 3rd person singular present tense form of the verb лежать.

So:

• лежать = to lie, to be lying
• лежит = he/she/it lies, is lying

Because коробка is singular, the verb is singular too.

A few related forms:

• я лежу = I am lying
• ты лежишь = you are lying
• они лежат = they are lying

Yes, this is a very common question. Russian often uses different verbs depending on an object's position:

• лежать = to lie
• стоять = to stand
• висеть = to hang

So лежит suggests the box is lying/resting on the floor, rather than being thought of as standing upright.

For many objects, Russian speakers choose the verb based on how the object is positioned:

• A book on a table often лежит
• A bottle on a table often стоит
• A picture on a wall висит

With a box, both лежит and стоит can be possible depending on how the speaker imagines it. In this sentence, the speaker is presenting it as lying on the floor.

Because Russian uses different cases after на depending on whether you mean location or motion.

• на + prepositional = on, at, in a place
• на + accusative = onto, to a place

Here the box is already located there, so Russian uses the location pattern: на полу.

Compare:

• Коробка лежит на полу. = The box is on the floor.
• Положи коробку на пол. = Put the box onto the floor.

So:

• на полу = on the floor
• на пол = onto the floor

This is a special location form used with some masculine nouns after в and на. In на полу, полу is a special locative/prepositional-type form meaning on the floor.

This is something learners usually just memorize as a set phrase:

• на полу = on the floor

There are other common examples of this pattern:

• в лесу = in the forest
• на берегу = on the shore
• в шкафу = in the wardrobe/cabinet

So even though it may look unusual at first, на полу is the normal form.

There is no article in Russian. Russian does not have words that work like English a/an and the in most ordinary sentences.

So картонная коробка can mean:

• a cardboard box
• the cardboard box

The exact meaning depends on context.

English requires an article, but Russian usually leaves that information unstated unless something else makes it clear.

No. Russian word order is much more flexible than English word order because the case endings show grammatical roles.

Картонная коробка лежит на полу is a normal, neutral order.

But you could also say:

• На полу лежит картонная коробка.

That version puts more focus on where the box is.

So the original sentence is not the only possible order; it is just the most straightforward, neutral one.

In a way, yes, but not as a separate word.

English says The cardboard box is lying on the floor. Russian does not need a separate present-tense to be here. The verb лежит already carries the idea of is lying.

So Russian does not say something like есть in this sentence.

That means:

• English: The box is lying...
• Russian: Коробка лежит...

This is completely normal in Russian.

The main stresses are:

картОнная корОбка лежИт на полУ

A rough pronunciation guide:

• картОнная = kar-TON-na-ya
• корОбка = ka-ROB-ka
• лежИт = lye-ZHEET
• на полУ = na pa-LOO

The stress matters a lot in Russian, so it is worth learning these together with the words.