It'd have to be this:
foreach ($id as $i) {
mysql_query("DELETE FROM areas WHERE (ID='$i')");
}
Of course, that will make n queries for n checked checkboxes...so you can improve that by using an OR statement, e.g.
DELETE FROM areas WHERE ID=1 Or ID=2 OR ID=5
but I'll leave that implementation to you.
Diego
P.S.: should there be single quotes around the ID field? If it's an ID number, it shouldn't have quotes...