It's a consequence of Russian's phonological rules
1) Stubborn Consonants
Most consonants followed by a softening vowel (я, е, и, ё, ю) turn soft (gets palatalized). But there are consonants that never change their hardness or softness even with a softening vowel in front of them. These are ш, ж, ц, щ, and ч. I like to call these "stubborn consonants". The first three are always hard while the last two are always soft.
So instead of being changed, they are actually the ones who change the vowel!
In the word "площадь", the letter "a" follows the stubborn letter щ. Because щ is always soft, it phonologically changes the "а" into a "я".
2) Unstressed Vowels
Most unstressed vowels change how they sound. An unstressed a and o turn into a lazy kind of "a". While unstressed и, е, and я turn into a lazy kind of "и". Because the "a" phonologically turned into a "я", being unstressed transformed it again into an "и".
And this why you hear an "i" there.
The Russian vowels change when they are stressed or not. So when a 'o' has the stress as in площадь the other vowel, here a will sound like something between i/e. If the 'a' would be stressed in this you would here something like 'plashad' since unstressed 'o''s sound like 'a' when people speek on a normal tempo. Bear in mind that Russians always know what the letters are, so when they talk slow площадь will sound like 'plo-shad'.