Write java code to design the following graphical user interface with main window having background color blue. The interface should contain 3 buttons for 'Yellow', 'red' and 'pink' When a button is clicked the background color of JTextArea found at the center of main window(JFrame) should be changed to that color.

To create a Java graphical user interface (GUI) as described, you can use the Swing library. Below is a sample code that sets up a `JFrame` with a blue background and three buttons ("Yellow", "Red", and "Pink"). When you click a button, the background color of a `JTextArea` in the center of the main window changes to the corresponding color.

Here's the complete code:

```java
import javax.swing.*;
import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

public class ColorChanger extends JFrame {
private JTextArea textArea;

public ColorChanger() {
// Set the title of the JFrame
setTitle("Color Changer");

// Set the default close operation
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

// Set the layout manager
setLayout(new BorderLayout());

// Create a JTextArea and set its properties
textArea = new JTextArea("Click a button to change my background color");
textArea.setEditable(false);
textArea.setBackground(Color.WHITE); // Initial background color
add(textArea, BorderLayout.CENTER);

// Create a JPanel to hold buttons
JPanel buttonPanel = new JPanel();
buttonPanel.setBackground(Color.BLUE); // Panel background will be blue

// Create buttons for different colors
JButton yellowButton = new JButton("Yellow");
JButton redButton = new JButton("Red");
JButton pinkButton = new JButton("Pink");

// Add action listeners for buttons
yellowButton.addActionListener(new ColorAction(Color.YELLOW));
redButton.addActionListener(new ColorAction(Color.RED));
pinkButton.addActionListener(new ColorAction(Color.PINK));

// Add buttons to the button panel
buttonPanel.add(yellowButton);
buttonPanel.add(redButton);
buttonPanel.add(pinkButton);

// Add button panel to the frame
add(buttonPanel, BorderLayout.SOUTH);

// Set the background color of the main window
getContentPane().setBackground(Color.BLUE);

// Set the window size and make it visible
setSize(400, 300);
setVisible(true);
setLocationRelativeTo(null); // Center the window on the screen
}

// Action listener class to change the background color of the JTextArea
private class ColorAction implements ActionListener {
private Color color;

public ColorAction(Color color) {
this.color = color;
}

@Override
public void actionPerformed(ActionEvent e) {
textArea.setBackground(color);
}
}

// Main method to run the application
public static void main(String[] args) {
// Use SwingUtilities to ensure thread safety
SwingUtilities.invokeLater(ColorChanger::new);
}
}
```

### Explanation:
1. **JFrame**: The main window which contains all the components.
2. **JTextArea**: A text area in the center to display information and change colors.
3. **JPanel**: A panel to hold the buttons at the bottom.
4. **JButton**: Three buttons to change the background color to Yellow, Red, and Pink.
5. **ActionListener**: When a button is clicked, it changes the background color of the `JTextArea` using the `setBackground()` method.
6. **setLayout()**: Used to set the layout of the `JFrame`.
7. **setSize() and setVisible()**: Methods to set the dimensions of the window and to make it visible.

To run this code:
- Copy and paste it into a Java IDE or a text file with a `.java` extension.
- Compile and run the program to see the GUI in action.