$DB = DB->connect(...);
my $size = sizeOfDB($DB);

sub sizeOfDB {
   my $db = shift;
   my $size = 0;
   my $st = $db->prepare('show table status');
   $st->execute;
   while (my $h = $st->fetchrow_hashref) {
      # other fields in %$h could be used, for example,
      # to limit the count to just certain tables.
      $size += $h->{Data_length} + $h->{Index_length};
   }
   $st->finish;
   return $size;
}