The 〜 shows the number of tatami mats, and the 畳 part is "tatami" of course. So, this is a counter for tatami mats. It is generally used to show how big an apartment or something is. Oh, your apartment is 12 tatami mats? Nice and big!
The reading is the same as the one you learned with the kanji.
This ten and a half mat room for just 10,000 yen a month is a first come, first served deal.