How To Find Minimum Height of the Triangle with Given Base and Area in Java?

The height of a triangle is the perpendicular distance from a vertex to the line containing the opposite side (which is the base). The height is also known as altitude.

What is Minimum Height?

The minimum height of a triangle refers to the shortest possible altitude (perpendicular distance) from a vertex to the opposite side (base).

The following diagram provides you with a clear idea of the triangle's height and its base:

A triangle is a polygon (a basic shape in geometry) that has three sides and three corners. The corners, also called vertices, are zero-dimensional points, while the sides connecting them, also called edges, are one-dimensional line segments.

As the problem specifies, find the minimum height of the triangle with a given base and area. The area of a triangle is defined as the total region (amount of space) that is enclosed by the three sides of any particular triangle.

The triangle has a standard way to calculate its area:

area = 1/2 x base x height

If the area and base are given, we can easily find the minimum height of the triangle.

Example 1

In this example, we use the standard area formula to determine the minimum height (shortest altitude) of a triangle by using the given triangle area 6 and base 14:

public class findHeight {
   public static void main(String args[]){
      double area = 6;
      System.out.println("The area of triangle: " + area);
	  
      double base = 14;
      System.out.println("The base of triangle: " + base);
      
      //find the height of the triangle using area and base
      double height = (2 * area) / base;
      System.out.println("The height of the triangle: " + height);
      
      //Find minimum height of triangle by using ceil() method
      double minHeight = Math.ceil(height);
      System.out.println("The minimum height of the triangle: " + minHeight);
   }
}

The above program produces the following output:

The area of triangle: 6.0
The base of triangle: 14.0
The height of the triangle: 0.8571428571428571
The minimum height of the triangle: 1.0

Example 2

In the example below, we define a method named findMinHeight() that takes two parameters, base and area. This method uses the standard area formula to calculate the minimum height of a triangle with a base of 6 and an area of 12:

public class findHeight {

    // Define a method to calculate the min height
    public static double findMinHeight(double base, double area) {
       return (area * 2) / base;
    }

    public static void main(String[] args) {
      double area = 12;
      double base = 6;
      System.out.println("The given area is: " + area);
      System.out.println("The given base is: " + base);

      //calling the findMinHeight() method to calculate minimum height
      System.out.println("The minimum height of the triangle: " + findMinHeight(base, area));
    }
}

Below is the output of the above program:

The area of a triangle: 12.0
The base of the triangle: 6.0
The minimum height of the triangle: 4.0