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

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:

triangle

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
Updated on: 2025-06-05T21:31:57+05:30

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