Mensor altitudinem, longitudinem et latitudinem metitur.

The sentence breaks down like this:

• Mensor = the subject
• altitudinem, longitudinem et latitudinem = the direct objects
• metitur = the verb

So the core pattern is:

[subject] [things being measured] [measures]

Latin often puts the verb near the end, so this word order is very normal.

Mensor means surveyor or measurer.

It is the subject because it is in the nominative singular, the case typically used for the subject of a sentence. Also, the verb metitur is third-person singular, so it matches a singular subject like mensor.

So:

• mensor = the surveyor / the measurer
• it is the one doing the action

Because metitur comes from a deponent verb: metior, metiri, mensus sum.

A deponent verb uses forms that look passive, but its meaning is active. So:

• metitur looks passive
• but it actually means he/she/it measures

This is very common in Latin and can feel strange to English speakers at first.

So here:

• metitur = measures
• not is measured

Yes. They are closely related in meaning.

• mensor = measurer / surveyor
• metitur = measures

So the sentence has a nice built-in connection between the person and the action. You can think of it almost like:

• the measurer measures

though in natural English we would usually say the surveyor measures.

Because all three are direct objects of metitur. They are the things being measured.

That is why they are all in the accusative singular:

• altitudinem = height
• longitudinem = length
• latitudinem = width / breadth

Their dictionary forms are:

• altitudo
• longitudo
• latitudo

The ending -inem is the accusative singular form of these third-declension nouns.

Because each word refers to one dimension considered as a single quantity:

• one height
• one length
• one width

English usually does the same in this kind of statement: He measures height, length, and width, not he measures heights, lengths, and widths.

Latin often coordinates a list the same way English does:

• A, B et C = A, B, and C

So:

• altitudinem, longitudinem et latitudinem

means:

• height, length, and width

Latin can also use other ways of joining words, such as repeated et or -que, but a single et before the last item is completely standard.

Because Latin does not have articles like English the or a/an.

So mensor can mean:

• a surveyor
• the surveyor

Which one is best depends on context. The same is true of the other nouns.

English has to choose an article, but Latin usually leaves that to the reader or listener to infer.

Yes. Latin word order is much freer than English word order because the endings show what each word is doing.

For example, the following would still mean essentially the same thing:

• Mensor altitudinem, longitudinem et latitudinem metitur.
• Altitudinem, longitudinem et latitudinem mensor metitur.
• Metitur mensor altitudinem, longitudinem et latitudinem.

That said, not every order sounds equally natural in every context. The version you have is straightforward and easy to read:

• subject first
• verb last

Here are the forms:

• mensor: nominative singular, third declension
• altitudinem: accusative singular of altitudo, third declension
• longitudinem: accusative singular of longitudo, third declension
• latitudinem: accusative singular of latitudo, third declension

So all the nouns in this sentence belong to the third declension.

That is useful to notice, because the sentence gives you a nice set of third-declension patterns.

A learner would normally memorize these dictionary forms:

• mensor, mensoris = surveyor, measurer
• altitudo, altitudinis = height
• longitudo, longitudinis = length
• latitudo, latitudinis = width, breadth
• metior, metiri, mensus sum = measure

That helps you connect the forms in the sentence to the vocabulary entries you would find in a dictionary.

Yes, that is a very close literal understanding.

Depending on context, it could also be understood more generally as:

• A surveyor measures height, length, and width
• The surveyor measures the height, length, and width

Latin does not force the article choice, so English translation may vary slightly even when the Latin stays the same.

In a simple Classical Latin-style pronunciation, you could say it roughly like this:

• MEN-sor al-ti-TU-di-nem, lon-gi-TU-di-nem et la-ti-TU-di-nem ME-ti-tur

A few helpful points:

• c is always hard, like k (not relevant here, but useful generally)
• ti in these words is usually pronounced clearly as ti
• vowels are pronounced more purely than in English
• the stress falls on -TU- in altitudinem, longitudinem, and latitudinem

Because the sentence is being specific. It names the three dimensions individually:

• height
• length
• width

That can make the statement clearer and more concrete. Instead of saying something general like the surveyor measures dimensions, it spells out exactly which dimensions are being measured.