This is a Java Program to find the area of a triangle using determinant method.
Formula for the area of a triangle using determinants
|x1 y1 1| Area = ±1/2 |x2 y2 1| |x3 y3 1|
The plus/minus in this case is meant to take whichever sign is needed so the answer is positive (non-negative). Do not say the area is both positive and negative.
Here is the source code of the Java Program to Compute the Area of a Triangle Using Determinants. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
//This is a java program to find the area of triangle using method of determinants import java.util.Random; public class Area_Triangle_Determinants { public static double determinant(double A[][], int N) { double det = 0; if (N == 1) { det = A[0][0]; } else if (N == 2) { det = A[0][0] * A[1][1] - A[1][0] * A[0][1]; } else { det = 0; for (int j1 = 0; j1 < N; j1++) { double[][] m = new double[N - 1][]; for (int k = 0; k < (N - 1); k++) { m[k] = new double[N - 1]; } for (int i = 1; i < N; i++) { int j2 = 0; for (int j = 0; j < N; j++) { if (j == j1) continue; m[i - 1][j2] = A[i][j]; j2++; } } det += Math.pow(-1.0, 1.0 + j1 + 1.0) * A[0][j1] * determinant(m, N - 1); } } return det; } public static void main(String args[]) { Random random = new Random(); int x1, x2, x3, y1, y2, y3; x1 = random.nextInt(10); x2 = random.nextInt(10); x3 = random.nextInt(10); y1 = random.nextInt(10); y2 = random.nextInt(10); y3 = random.nextInt(10); double[][] mat = new double[3][3]; mat[0][0] = x1; mat[0][1] = y1; mat[0][2] = 1; mat[1][0] = x2; mat[1][1] = y2; mat[1][2] = 1; mat[2][0] = x3; mat[2][1] = y3; mat[2][2] = 1; System.out .println("The matrix formed by the coordinates of the triangle is: "); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) System.out.print(mat[i][j] + " "); System.out.println(); } double det = determinant(mat, 3) * 0.5; if (det < 0) System.out.println("The Area of the triangle formed by (" + x1 + "," + y1 + "), (" + x2 + "," + y2 + "), (" + x3 + "," + y3 + ") = " + (det * -1)); else System.out.println("The Area of the triangle formed by (" + x1 + "," + y1 + "), (" + x2 + "," + y2 + "), (" + x3 + "," + y3 + ") = " + det); } }
Output:
$ javac Area_Triangle_Determinants.java $ java Area_Triangle_Determinants The matrix formed by the coordinates of the triangle is: 3.0 4.0 1.0 6.0 4.0 1.0 3.0 9.0 1.0 The Area of the triangle formed by (3,4), (6,4), (3,9) = 7.5
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