Tessera triangula est.

• tessera is the subject: the thing being talked about.
• triangula is an adjective describing the subject.
• est means is.

So the structure is essentially:

subject + adjective + is

That is why the sentence means that the tessera is triangular.

Because it has to agree with tessera.

In Latin, adjectives usually match the nouns they describe in:

• gender
• number
• case

Here:

• tessera is feminine
• singular
• nominative

So the adjective must also be feminine singular nominative, which gives triangula.

Triangulus is the masculine form.

The adjective has different forms:

• triangulus = masculine
• triangula = feminine
• triangulum = neuter

Since tessera is feminine, Latin uses triangula, not triangulus.

It is nominative singular.

You can tell because it is the subject of the sentence, and subjects in Latin are normally in the nominative case.

Also, tessera is a first-declension noun, and -a is a very common nominative singular ending for first-declension nouns.

Latin word order is much more flexible than English word order.

English strongly prefers:

• The tile is triangular

Latin can say:

• Tessera triangula est
• Tessera est triangula
• Triangula tessera est

All of these can mean basically the same thing.

That said, putting the verb at the end is very common in Latin, especially in simple textbook-style sentences.

Yes.

That would still mean the same thing. Latin allows this kind of variation because the word endings already show the grammatical relationships.

Sometimes a different word order can slightly change emphasis, but in a simple sentence like this, the meaning stays the same.

Because Latin has no articles.

English distinguishes:

• a triangular tile
• the triangular tile

Latin usually does not mark that difference with a separate word. So tessera triangula est could be translated into English with whichever article best fits the context:

• A triangular tile is...
• The tile is triangular

The exact English wording depends on the situation.

Here it is an adjective.

It is describing tessera, and it agrees with it in gender, number, and case.

A learner might notice that some Latin adjective forms can also look like nouns in other contexts, but in this sentence triangula is clearly an adjective meaning triangular.

Yes, in this kind of sentence they do.

With the verb est, when an adjective describes the subject, that adjective is in the nominative too. This is often called a predicate adjective.

So:

• tessera = nominative subject
• triangula = nominative adjective linked to the subject by est

That is why both words have nominative singular feminine forms.

Often, yes.

Latin sometimes omits forms of to be when the meaning is still clear. So in some contexts, you might see:

Tessera triangula

and understand it as: The tile is triangular.

But in beginner sentences, est is usually included to make the structure clear.

A rough classical pronunciation would be:

TESS-eh-ra tree-AHN-goo-la est

A few helpful points:

• tessera begins with a clear t
• triangula has a hard g, as in go
• vowel sounds are usually pronounced clearly, not reduced as often happens in English

If you want an even rougher English guide: TESS-eh-ra tree-ANG-goo-la est

In this case, yes: tessera is a feminine first-declension noun.

But it is worth remembering that -a does not absolutely guarantee feminine gender in every Latin word. There are exceptions, especially among nouns referring to male people, such as some occupations.

Still, for a beginner, -a = often feminine first declension is a very useful pattern, and tessera follows that normal pattern.