Late to the party, but here is an alternative, using XML::Twig - somewhat less code, but handles only one file at a time:

#!/bin/perl -w
use strict;
use XML::Twig;

my $twig= new XML::Twig( 
            twig_handlers =>                   
               { _all_ => \&Piece_handler , # Call for each 'Program' 
+elemetn
               }
    );          

$twig->parsefile( shift @ARGV );    # build the twig
#-------------------------------------------------
sub Piece_handler{
   my( $twig, $p)= @_;                      # handlers params are alwa
+ys
                                                 # the twig and the el
+ement
     return unless $p->text && $p->text=~/design/;

     print $p->tag , ":",$p->text,"\n";
     #Traverse and print ancestor tags 
     for (my $ancestor = $p->parent; defined $ancestor; $ancestor=$anc
+estor->parent()){
       print "\tParent : ", $ancestor->tag, "\n";
     }
     
      $p->cut;  # This one is processed, delete from tree ..
}
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Produces the following (After adding a proper closing </root> tag to the second example):

$ perl xmlt.pl xmldata2.xml 
para:This is a design XZY document for Project
    Parent : root

$ perl xmlt.pl xmldata.xml 
header:
                   This is a design XZY document for Project
                
    Parent : sect
    Parent : part
    Parent : root
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