编写一个java程序将求和、求平均值、排序等类放入“算术包”中，将计算三角形面积，计算矩形面积等类放入“几何包”，并在”应用包“中的测试类中计算几个图形的面积平均值等。

在Java中，为了组织代码并增强模块化，我们可以创建包（packages）来分别存放相关的类。首先，我们需要创建三个包：`算术包`、`几何包`和`应用包`。

1. **算术包** (ArithmeticPackage):
- 定义一个`SumCalculator.java` 类用于求和操作，如整数或浮点数数组的总和。

   package 算术包;
   
   public class SumCalculator {
       public static double sum(double[] numbers) {
           double total = 0;
           for (double number : numbers) {
               total += number;
           }
           return total;
       }
   }

- 同样地，可以有`AverageCalculator.java` 类计算平均值。

2. **几何包** (GeometryPackage):
- 创建`TriangleAreaCalculator.java` 和 `RectangleAreaCalculator.java` 分别计算三角形和矩形的面积。

   package 几何包;
   
   public class TriangleAreaCalculator {
       public static double area(double base, double height) {
           return 0.5 * base * height;
       }
   }

   public class RectangleAreaCalculator {
       public static double area(double length, double width) {
           return length * width;
       }
   }

3. **应用包** (ApplicationPackage):
- 在这里，我们编写`TestGeometry.java` 或者类似名称的测试类。

   package 应用包;
   
   import 算术包.SumCalculator;
   import 几何包.TriangleAreaCalculator;
   import 几何包.RectangleAreaCalculator;

   public class TestGeometry {
       public static void main(String[] args) {
           double[] numbers = {1, 2, 3, 4, 5};
           System.out.println("Numbers sum: " + SumCalculator.sum(numbers));

           double triangleBase = 5, triangleHeight = 3;
           double triangleArea = TriangleAreaCalculator.area(triangleBase, triangleHeight);
           System.out.println("Triangle area: " + triangleArea);

           double rectangleLength = 10, rectangleWidth = 6;
           double rectangleArea = RectangleAreaCalculator.area(rectangleLength, rectangleWidth);
           System.out.println("Rectangle area: " + rectangleArea);

           // 计算平均面积
           double[] areas = {triangleArea, rectangleArea};
           double averageArea = SumCalculator.sum(areas) / areas.length;
           System.out.println("Average area: " + averageArea);
       }
   }