Developing a plugin – link to pages

I am a beginner to WP plugin development and PHP. I am developing (or trying to develop) a plugin. My main page (called merchants- code below) is working as expected. My need is to produce search results in the same or another page when you click the Search button. Details as follows:

Plugin Name: Merchants
WP Version : 3.7.1
Web Server: WAMP 2.2, Localhost

Database:

-- Table structure for table <code>directory</code>

CREATE TABLE IF NOT EXISTS <code>directory</code> (
  <code>directory_id</code> int(5) NOT NULL AUTO_INCREMENT,
  <code>merchant</code> varchar(50) NOT NULL,
  <code>category</code> varchar(50) NOT NULL,
  <code>area</code> varchar(50) NOT NULL,
  PRIMARY KEY (<code>directory_id</code>)
) ENGINE=InnoDB  DEFAULT CHARSET=latin1 AUTO_INCREMENT=7 ;

-- Dumping data for table <code>directory</code>

INSERT INTO <code>directory</code> (<code>directory_id</code>, <code>merchant</code>, <code>category</code>, <code>area</code>) VALUES
(1, 'Acapps', 'IT Services', 'Cape Town CBD'),
(2, 'Octagon Property', 'Real Estate', 'Green Point'),
(3, 'JFM Solutions', 'IT Services', 'Bellville'),
(4, 'Lollas Cleaning', 'Health & Hygiene', 'Belhar'),
(5, 'Genana B C', 'IT Services', 'Belhar'),
(6, 'Pick n Pay', 'Supermarket', 'Green Point');

PHP CODE

The main page is called merchants.php:

<?PHP

/*
Plugin Name: Merchants
Description: Custom plugin to manage merchants on my future website

*/

function list_merchants(){
	global $wpdb;

	//Get specified fields from DB
	$merchants	=	$wpdb->get_results("SELECT * FROM directory");

	//Create a search form, start populating variable $show for shortcode implementation later
	$show	=	"<form method='POST' action='http://localhost/lab/search.php'>";

	$show	.=	"<select name='areas'>
					<option>Belhar<option>
					<option>Bellville<option>
					<option>Cape Town CBD<option>
					<option>Green Point<option>
				</select>";

	$show	.=	"<input type='submit' value='Search' /></form>";

	//Create a table to show results
	$show	.=  "<table cellspacing='5' cellpadding='5' border='2'>";

	$show	.=	"<th>COMPANY</th>	<th>CATEGORY</th>	<th>AREA</th>";

	//walkthrough array $merchant to display all merchants in DB
	foreach( $merchants AS $merchants){

		$show .=	"<tr><td>" . $merchants->merchant . "</td><td>" . $merchants->category . "</td><td>" . $merchants->area . "</td></tr>";

	}

	$show	.=	"</table>";

	return $show;
}

add_shortcode( 'merchants', 'list_merchants');

?>

..and finally the code I am attempting to get result from (named search.php)

<?PHP

function search_by_area(){
	global $wpdb;

	//Get results matching keyword
	If (ISSET($_POST['areas'])){
		$keyword	=	$_POST['areas'];
		$merchants_result	=	$wpdb->get_results("SELECT * FROM directory WHERE area WHERE area REGEXP '$keyword' ORDER BY merchant");
	}

	Else {
		$merchants_result	=	$wpdb->get_results("SELECT * FROM directory");
		}

	//Create a table to show results
	$show_result	.=  "<table cellspacing='5' cellpadding='5' border='2'>";

	$show_result	.=	"<th>COMPANY</th>	<th>CATEGORY</th>	<th>AREA</th>";

	//walkthrough array $merchant to display all merchants in DB
	foreach( $merchants_result AS $merchants_result){

		$show_result .=	"<tr><td>" . $merchants_result->merchant . "</td><td>" . $merchants_result->category . "</td><td>" . $merchants_result->area . "</td></tr>";

	}

	$show_result	.=	"</table>";

	return $show_result;
}

//add_shortcode( 'search', 'search_by_area');

?>

Remember the goal is to show results in the same or another page when you click on my Search button. Your contribution is really appreciated.