Learn Turkish: Anahtar halının altında.

In Turkish, spatial words like "under" or "inside" act like nouns. The word alt means "bottom" or "underside". To say something is "under" the rug, you literally say it is "at its underside". So, altında is made of alt (bottom) + ı (its) + n (buffer letter) + da (at).

Why is the ending "-nın" attached to "halı"?

Because we are literally saying "at the rug's underside", we must use the possessive (genitive) case. Halı means "rug", and adding -nın makes it "the rug's". The first n in -nın is a buffer letter used because halı ends in a vowel.

Why is there an "n" before the "-da" in "altında"?

When you attach a location suffix like -da (at/on/in) to a word that already has a third-person possessive ending like the -ı in altı, Turkish requires the buffer letter n between them. This makes it easier to pronounce: alt + ı + n + da.

Where are the words for "the" and "is" in this sentence?