functions.php

<?php
/* =BEGIN: Check If Page Is Parent/Child/Ancestor
    Source: http://www.stemlegal.com/greenhouse/2012/checking-ancestor-and-parent-pages-in-wordpress/
   ---------------------------------------------------------------------------------------------------- */
    function is_tree( $page_id_or_slug ) {
	    global $post;

	    if ( !is_numeric( $page_id_or_slug ) ) { // Used this code to change a slug to an ID, but had to change is_int to is_numeric for it to work: http://bavotasan.com/2011/is_child-conditional-function-for-wordpress/
	        $page = get_page_by_path( $page_id_or_slug );
	        $page_id_or_slug = $page->ID;
	    }

	    if ( is_page( $page_id_or_slug ) )
	        return true;

	    $anc = get_post_ancestors( $post->ID );
	    foreach ( $anc as $ancestor ) {
	        if ( is_page() && $ancestor == $page_id_or_slug ) {
	            return true;
	        }
	    }
	    return false;
	}

?>

sidebar.php

<?php if ( is_tree( 'subpage' ) ) { // Using the slug /subpage/, but you could also use the ID of /subpage/ ?>
    [[... insert your code here ...]]
<?php } ?>