Learn Icelandic: Læknirinn mælir stærð augnanna. - The doctor measures the size of the eyes.

Auga is a weak neuter noun. For the small closed set of body parts in this category, an "n" is inserted into the stem in the genitive plural, making it augna (of eyes). Adding the definite genitive plural suffix -nna gives us the final form augnanna (of the eyes).

Why is augnanna in the genitive case?

It expresses relation or possession, directly translating to "of the eyes" in English. In Icelandic, the word expressing "of [something]" immediately follows the main noun and takes the genitive case.

Why is "the size" translated as just stærð instead of the definite stærðin?

When a noun is followed by a possessive modifier in the definite genitive case (like augnanna), the first noun almost always drops its own definite article. The definiteness of the whole phrase is anchored by the second word.

What case is stærð in this sentence?

It is in the accusative case because it is the direct object of the verb mæla (to measure). For the feminine noun stærð, the accusative form happens to be identical to the nominative.