使用开闭原则、MVC结构、GUI，求底为三角形、梯形、园的柱形的体积。

根据开闭原则，我们需要使用抽象类或接口来定义计算体积的方法。同时，使用MVC结构将计算逻辑与界面展示分离开来，方便维护和拓展。

首先，我们可以定义一个Shape接口，包含计算体积的方法：

public interface Shape {
    double getVolume(double height);
}

然后，我们可以针对不同的底形状（三角形、梯形、园）分别实现一个类来实现Shape接口：

public class Triangle implements Shape {
    private double base;
    private double height;

    public Triangle(double base) {
        this.base = base;
    }

    @Override
    public double getVolume(double height) {
        return base * height / 2 * height;
    }
}

public class Trapezium implements Shape {
    private double upperBase;
    private double lowerBase;
    private double height;

    public Trapezium(double upperBase, double lowerBase) {
        this.upperBase = upperBase;
        this.lowerBase = lowerBase;
    }

    @Override
    public double getVolume(double height) {
        return (upperBase + lowerBase) * height / 2 * height;
    }
}

public class Circle implements Shape {
    private double radius;

    public Circle(double radius) {
        this.radius = radius;
    }

    @Override
    public double getVolume(double height) {
        return Math.PI * radius * radius * height;
    }
}

最后，我们可以使用GUI来展示界面，并将计算逻辑与界面展示分离开来，实现MVC结构。这里给出一个简单的Swing GUI实现：

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

public class ShapeVolumeCalculator extends JFrame {

    private JTextField heightField;
    private JTextField baseField;
    private JTextField upperBaseField;
    private JTextField lowerBaseField;
    private JTextField radiusField;
    private JComboBox<String> shapeBox;
    private JLabel resultLabel;

    public ShapeVolumeCalculator() {
        setTitle("Shape Volume Calculator");
        setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);

        JPanel mainPanel = new JPanel(new GridLayout(7, 2, 10, 10));

        JLabel shapeLabel = new JLabel("Shape:");
        shapeBox = new JComboBox<>(new String[]{"Triangle", "Trapezium", "Circle"});
        mainPanel.add(shapeLabel);
        mainPanel.add(shapeBox);

        JLabel heightLabel = new JLabel("Height:");
        heightField = new JTextField();
        mainPanel.add(heightLabel);
        mainPanel.add(heightField);

        JLabel baseLabel = new JLabel("Base:");
        baseField = new JTextField();
        mainPanel.add(baseLabel);
        mainPanel.add(baseField);

        JLabel upperBaseLabel = new JLabel("Upper Base:");
        upperBaseField = new JTextField();
        mainPanel.add(upperBaseLabel);
        mainPanel.add(upperBaseField);

        JLabel lowerBaseLabel = new JLabel("Lower Base:");
        lowerBaseField = new JTextField();
        mainPanel.add(lowerBaseLabel);
        mainPanel.add(lowerBaseField);

        JLabel radiusLabel = new JLabel("Radius:");
        radiusField = new JTextField();
        mainPanel.add(radiusLabel);
        mainPanel.add(radiusField);

        JButton calculateButton = new JButton("Calculate");
        calculateButton.addActionListener(new ActionListener() {
            @Override
            public void actionPerformed(ActionEvent e) {
                Shape shape = null;
                switch (shapeBox.getSelectedIndex()) {
                    case 0:
                        shape = new Triangle(Double.parseDouble(baseField.getText()));
                        break;
                    case 1:
                        shape = new Trapezium(Double.parseDouble(upperBaseField.getText()), Double.parseDouble(lowerBaseField.getText()));
                        break;
                    case 2:
                        shape = new Circle(Double.parseDouble(radiusField.getText()));
                        break;
                }
                double volume = shape.getVolume(Double.parseDouble(heightField.getText()));
                resultLabel.setText("Volume: " + volume);
            }
        });
        mainPanel.add(new JLabel());
        mainPanel.add(calculateButton);

        resultLabel = new JLabel();
        mainPanel.add(resultLabel);

        add(mainPanel);
        pack();
        setLocationRelativeTo(null);
        setVisible(true);
    }

    public static void main(String[] args) {
        new ShapeVolumeCalculator();
    }
}

这样，我们就实现了一个根据开闭原则、MVC结构、GUI展示来计算底为三角形、梯形、园的柱形的体积的程序。