Я не знаю точную высоту полки, но её длина — почти метр.

Because знать takes a direct object: you know something.
Here, the thing being known is точная высота полки.

So:

• высота → accusative высоту
• точная → accusative feminine точную

The adjective must agree with the noun in gender, number, and case.

Russian often expresses of relationships with the genitive case.

So:

• высота полки = the height of the shelf
• literally, height shelf-of

The basic noun is полка, and its genitive singular form is полки.

Here it is genitive singular: of the shelf.

That form can also be nominative plural in other contexts, so learners often get confused. Context tells you which one it is. In this sentence, after высота, the natural reading is height of the shelf, not shelves.

Because it has to match высоту.

The noun высота is:

• feminine
• singular
• accusative

So the adjective точный changes to the matching form точную.

Russian nouns have grammatical gender. Полка is feminine, so when Russian refers back to it, её is the normal possessive form.

For things and objects, Russian still uses the gender of the noun:

• стол is masculine
• книга is feminine
• окно is neuter

So её длина means its length, even though the form looks like her to an English speaker.

Yes, sometimes.

You could say:

• ...но длина — почти метр

If the context is clear, that sounds fine. But её makes the reference more explicit and can make the sentence easier to follow.

In present-tense sentences like X is Y, Russian usually leaves out the verb to be.

So instead of saying something equivalent to её длина есть почти метр, Russian normally says:

• её длина — почти метр

The dash often marks this relationship in writing, especially when the second part is a noun, a number, or a measurement.

Because Russian has no articles.

So метр can mean:

• a meter
• the meter

depending on context.

Here почти метр naturally means almost a meter.

Because почти does not force the genitive case. It is just an adverb meaning almost.

So you keep the normal singular form:

• почти метр = almost a meter

A useful comparison:

• около метра = about a meter
  Here около is a preposition, and it does require the genitive, so you get метра.

That is why почти метр and около метра look different.

Yes. In many Russian texts, ё is written as е.

So you may see:

• её длина
• ее длина

Both mean the same thing, but the pronunciation is still её, with yo.

Yes. Russian word order is flexible.

The given sentence is neutral and natural:

• Я не знаю точную высоту полки, но её длина — почти метр.

But you could also say:

• Точную высоту полки я не знаю...

That puts more emphasis on the exact height.

So the basic meaning stays the same, but the focus changes.

They are two different measurements:

• высота = height
• длина = length

So the sentence contrasts one dimension with another.

A subtle point: высота полки usually means the shelf’s own height or vertical dimension, not the height at which the shelf is mounted on a wall. If you wanted how high the shelf is located, Russian would normally phrase that differently.

Но is the most straightforward choice because it marks a clear contrast:

• I do not know one measurement,
• but I do know another.

А can also connect contrasting ideas, but it often feels more like setting two facts side by side rather than giving a stronger but contrast. In this sentence, но is the most natural default choice.

A useful stress-marked version is:

Я не зна́ю то́чную высоту́ по́лки, но её длина́ — почти́ ме́тр.

A few helpful notes:

• зна́ю has stress on зна́-
• то́чную has stress on the first syllable
• высоту́ has stress on the last syllable
• по́лки has stress on the first syllable
• её is pronounced roughly ye-YO
• длина́ has stress on the last syllable
• почти́ has stress on the last syllable
• ме́тр has stress on the only vowel