我们可以使用Java语言中的Graphics2D类来绘制多边形与矩形，并使用循环和数组来计算所有多边形的点的最小和最大值。最后，根据这些值来绘制一个围绕多边形的矩形。

以下为简单示例代码：

import java.awt.*;
import javax.swing.*;

public class PolygonBlocker extends JPanel {

   private int[][] points = new int[][]{{50, 100}, {150, 50}, {250, 100}, {300, 200}, {100, 200}};

   public void paint(Graphics g) {
      super.paint(g);
      Graphics2D g2d = (Graphics2D) g;

      //绘制原始多边形
      Polygon polygon = new Polygon();
      for(int i = 0; i < points.length; i++) {
         polygon.addPoint(points[i][0], points[i][1]);
      }
      g2d.draw(polygon);

      //计算多边形的最小和最大值
      int minX = points[0][0];
      int maxX = points[0][0];
      int minY = points[0][1];
      int maxY = points[0][1];
      for(int i = 1; i < points.length; i++) {
         int x = points[i][0];
         int y = points[i][1];
         if(x < minX) minX = x;
            else if(x > maxX) maxX = x;
         if(y < minY) minY = y;
            else if(y > maxY) maxY = y;
      }

      //绘制矩形
      g2d.drawRect(minX, minY, maxX - minX, maxY - minY);
   }

   public static void main(String[] args) {
      JFrame frame = new JFrame("Polygon Blocker");
      frame.add(new PolygonBlocker());
      frame.setSize(