# C > Mathematics Code Examples

## Program to calculate Area of a Polygon

``` Program to calculate Area of a Polygon /* Given the coordinates of the vertices of a convex polygon, calculate its area and perimeter. Subdivide it into triangles and calculate the area of each triangle with Heron's formula. Requires data file pvert.txt containing coordinates of each vertex. Example of data for a polygon with 5 vertices: 3 7 6 4 3 -2 -6 1 -6 7 */ #include <stdio.h> #include <stdlib.h> #include <math.h> #define MAX_VERT 50 enum {x, y}; typedef struct triangle { double v1[2]; double v2[2]; double v3[2]; } triangle; double area(triangle a); double perimeter(double *vertices, int size); double side(double *p1, double *p2); int main(void) { int n, idx; int triangles; int index; int xycount; double xy; double triangle_area; double polygon_area; double perim; double polygon_vertices[MAX_VERT] = {0.0}; triangle a; FILE *data; xycount = 0; polygon_area = 0; if((data = fopen("pvert.txt", "r")) == NULL) { fprintf(stderr, "can't open data file "); exit(EXIT_FAILURE); } /* Read x-y coordinates of the vertices of the polygon from a file. */ while(fscanf(data, "%lf", &xy) == 1) polygon_vertices[xycount++] = xy; fclose(data); idx = 0; /* triangles in polygon = vertices - 2 */ triangles = (xycount / 2) - 2; putchar(' '); for(index = 2, idx = 0; idx < triangles; index += 2, ++idx) { /* Load vertices of a triangle into struct. 1st vertex of the polygon will be the 1st vertex of each triangle. index holds the starting index of each consecutive set of triangle vertices after the 1st. */ a.v1[x] = polygon_vertices[0]; a.v1[y] = polygon_vertices[1]; a.v2[x] = polygon_vertices[index+0]; a.v2[y] = polygon_vertices[index+1]; a.v3[x] = polygon_vertices[index+2]; a.v3[y] = polygon_vertices[index+3]; /* calculate the area of the triangle */ triangle_area = area(a); printf("area of triangle = %.2f ", triangle_area); /* add triangle area to polygon area */ polygon_area += triangle_area; } printf(" area of polygon = %.2f ", polygon_area); /* calculate the perimeter of the polygon */ perim = perimeter(polygon_vertices, xycount); printf("perimeter of polygon = %.2f ", perim); return 0; } /* calculate triangle area with Heron's formula */ double area(triangle a) { double s1, s2, s3, S, area; s1 = side(a.v1, a.v2); s2 = side(a.v2, a.v3); s3 = side(a.v3, a.v1); S = (s1 + s2 + s3) / 2; area = sqrt(S*(S - s1)*(S - s2)*(S - s3)); return area; } /* calculate polygon perimeter */ double perimeter(double *vertices, int size) { int idx, jdx; double p1[2], p2[2], pfirst[2], plast[2]; double perimeter; perimeter = 0.0; /* 1st vertex of the polygon */ pfirst[x] = vertices[0]; pfirst[y] = vertices[1]; /* last vertex of polygon */ plast[x] = vertices[size-2]; plast[y] = vertices[size-1]; /* calculate perimeter minus last side */ for(idx = 0; idx <= size-3; idx += 2) { for(jdx = 0; jdx < 4; ++jdx) { p1[x] = vertices[idx]; p1[y] = vertices[idx+1]; p2[x] = vertices[idx+2]; p2[y] = vertices[idx+3]; } perimeter += side(p1, p2); } /* add last side */ perimeter += side(plast, pfirst); return perimeter; } /* calculate length of side */ double side(double *p1, double *p2) { double s1, s2, s3; s1 = (p1[x] - p2[x]); s2 = (p1[y] - p2[y]); s3 = (s1 * s1) + (s2 * s2); return sqrt(s3); } ```