This is a Java Program to find the area of a triangle using determinant method.

Formula for the area of a triangle using determinants

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:

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$ 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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