How to get panels to occupy all available space and components in the center?

I am writing a program, which has a toolbar panel at the bottom (using BorderLayout) of the content pane, and a main panel at the center of the content pane.
The main panel has a label at the bottom (using BorderLayout) and a "view" panel in the center which has a cardLayout. The view panel has two components at the moment, a label and a text area.
The problem is that except for the toolbar panel, all other panels do not occupy all the space available (see diagrams attached).
I know this problem is solved by using a different layout manager, but the problem is i'm not sure which one would be the best to use here. I could use some advice.

I've attached three things
-a simplified compilable version of the code, to illustrate the problem
-a screenshot of what I get when I run the code
-an image of the kind of layout I want.

Thanks for your help.

Code

Code:

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import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.FlowLayout;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JTextArea;


public class LayoutProblem {
        private JFrame window;
        private JButton button;
        private JLabel label;
       
        private JPanel contentPanel;
        private JPanel middlePanel;
        private JPanel bottomPanel;
        private JLabel textAreaLabel;
        private JTextArea textArea;
       
        public LayoutProblem()
        {
                window = new JFrame("Window");
                window.setSize(600,400);
                window.setVisible(true);
                window.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
               
               
                bottomPanel = new JPanel();
                bottomPanel.setBackground(Color.BLUE);
                button = new JButton("Button");
                bottomPanel.add(button);
                window.getContentPane().add(bottomPanel, BorderLayout.SOUTH);
               
                contentPanel = new JPanel();
                       
                        label = new JLabel ("Label");
                       
                        middlePanel = new JPanel();
                                middlePanel.setBackground(Color.RED);
                                middlePanel.setLayout(new FlowLayout(FlowLayout.CENTER));
                               
                                textAreaLabel = new JLabel("Hi");
                                textArea = new JTextArea("Stuff Stuff Stuff");
                               
                                middlePanel.add(textAreaLabel);
                                middlePanel.add(textArea);
                               
                        contentPanel.add(middlePanel,BorderLayout.CENTER);
                        contentPanel.add(label,BorderLayout.SOUTH);
                       
                        window.getContentPane().add(contentPanel,BorderLayout.CENTER);
        }
       
        public static void main(String args[])
        {
                new LayoutProblem();
        }
}

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What I get:
Attachment 1894

What I want: (Sorry, the image kinda burns the eyes a bit)
Attachment 1895