Pattern Factory PHP, what advantages Can I have?

I Want to improve my knowledge about PHP Pattern and Architecture. I create a stupid example to use Factory Pattern

This is my Code:

index.php

$shape = Shape::getShape('circle', 3);
echo $shape->getArea();

shapes.php

class Shape
{

    public static function getShape($type, $num)
    {
        switch ($type) {
            case 'circle':
                return new Circle($num);
                break;
            case 'square':
                return new Square($num);
                break;
            default:
                throw new Exception("Unrecognized shape");
        }
    }
}


abstract class Form{
    abstract public function getArea();
}

class Circle extends Form{
    protected $_type = "Circle";
    private $area;
    /**
     * circle constructor.
     * @param $area
     */
    public function __construct($area)
    {
        $this->area = $area;
    }
    public function getArea(){
          return $this->area*pi();
    }
}

Where is the advanteges to use this approach ?

I could do it, to create Circle Object

$circle = new Circle(3);
echo $circle->getArea();

The Only Advantage that I can see with use Factory Pattern is that, I could don't know which Shape the user Want.