C Program to Find the Area of a Triangle Using Determinants

This is a C program to find the area of 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 source code of the C Program to Compute the Area of a Triangle Using Determinants. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include <string.h>
```
```
#include <stdio.h>
```
```
#include <stdlib.h>
```
```
 
```
```
int i, j, c;
```
```
double det(int n, double mat[3][3]) {
```
```
    double submat[3][3];
```
```
    float d;
```
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    for (c = 0; c < n; c++) {
```

        int subi = 0; //submatrix's i value

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        for (i = 1; i < n; i++) {
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            int subj = 0;
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            for (j = 0; j < n; j++) {
```
```
                if (j == c)
```
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                    continue;
```

                submat[subi][subj] = mat[i][j];

```
                subj++;
```
```
            }
```
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            subi++;
```
```
 
```
```
        }
```

        d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat));

```
    }
```
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    return d;
```
```
}
```
```
int main(int argc, char **argv) {
```
```
 
```

    printf("Enter the points of the triangle:\n");

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    int x1, x2, x3, y1, y2, y3;
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    scanf("%d", &x1);
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    scanf("%d", &y1);
```
```
 
```
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    scanf("%d", &x2);
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    scanf("%d", &y2);
```
```
 
```
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    scanf("%d", &x3);
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    scanf("%d", &y3);
```
```
 
```
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    double mat[3][3];
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    mat[0][0] = x1;
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    mat[0][1] = y1;
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    mat[0][2] = 1;
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    mat[1][0] = x2;
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    mat[1][1] = y2;
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    mat[1][2] = 1;
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    mat[2][0] = x3;
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    mat[2][1] = y3;
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```
    mat[2][2] = 1;
```
```
 
```

    printf("\nMatrix formed by the points: \n");

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    for (i = 0; i < 3; i++) {
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```
        for (j = 0; j < 3; j++) {
```
```
            printf("%lf ", mat[i][j]);
```
```
        }
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        printf("\n");
```
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    }
```
```
 
```

    float determinant = det(3, mat) * 0.5;

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    if (determinant < 0)
```
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        printf(
```

                "The area of triangle formed by (%d, %d), (%d, %d), (%d, %d) = %lf ",

                x1, y1, x2, y2, x3, y3, (determinant * -1));

```
    else
```
```
        printf(
```

                "The area of triangle formed by (%d, %d), (%d, %d), (%d, %d) = %lf ",

                x1, y1, x2, y2, x3, y3, (determinant));

```
    return 0;
```
```
}
```

Output:

$ gcc TraingleArea.c
$ ./a.out
 
Enter the points of the triangle:
3 4
6 4
3 9
 
Matrix formed by the points: 
3 4 1 
6 4 1 
3 9 1 
The Area of the triangle formed by (3,4), (6,4), (3,9) = 7.5

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