First, you didn't capture anything, which is how $n variables are populated. Put parenthesis around what you want to be captured into $1
if ($line =~ /([a-z]ar)i/) { print "$1\n" }
I've removed the /g which is unneeded (and with potential for trouble†) here.
Next, your pattern requires and captures one letter followed by literal ar, no more no less. That won't capture near, nor will it capture parked (it'll get par only). It will not even match a word that starts with ar, since it requires that there is a letter before ar. You need to use quantifiers, to tell it how many times to match a letter. And you also want to find all matches.
One way is to scoop them all up by providing the list context and /g (global) modifier
my @words = $line =~ /([a-z]*ar[a-z]*)/gi;
print "$_\n" for @words;
The [a-z]* means to match a letter, zero-or-more times. So an optional string of letters. We also added an optional string of letters after ar. The /g makes it continue through the string after a match, to find all such patterns. In the list context the list of matches is returned.
Or, you can match in scalar context like in the first example, but in a while loop
while ($line =~ /([a-z]*ar[a-z]*)/gi) { print "$1\n" }
Here /g does something different. It matches a pattern once and returns true, the while condition is true and we print. Then it comes back and looks for a match from where it matched previously ... and keeps doing this until there are no more matches.
This is complex behavior altogether. From Regexp Quote-Like Operators in perlop
The /g modifier specifies global pattern matching--that is, matching as many times as possible within the string. How it behaves depends on the context. In list context, it returns a list of the substrings matched by any capturing parentheses in the regular expression. If there are no parentheses, it returns a list of all the matched strings, as if there were parentheses around the whole pattern.
In scalar context, each execution of m//g finds the next match, returning true if it matches, and false if there is no further match. [...]
Read about this in more detail and in a tutorial manner in perlretut, under "Global matching."
† Note on using /g modifier in scalar context
I've used that above, in while (/.../g), what is a very common way to hop over all occurrences of the pattern in a string, each time giving us control in the while body.
While this use is intended and idiomatic, the use of /g in scalar context can bring subtle trouble when not in the loop condition: the next regex with /g on this variable will continue from the previous match, not from the string's beginning, what may be unexpected.
That "next regex" may also simply be that same expression -- in the next pass of some larger loop in which our expression happens to be, and this holds across function calls as well. Consider
use warnings;
use strict;
use feature 'say';
my $s = q(one two three);
sub func { say $1 if $_[0] =~ /(\w+)/g }; # /g may be of great consequence!
for (1..4) {
# ... perhaps much, much later ...
func($s);
}
This loop prints lines one, then two, then three, and that's that. This (working) example is so bare bones that it is artificial bit I hope that it conveys that /g in scalar context may surprise.
For one thing, it is not uncommon to see /g on a regex in an if condition being plain wrong.