In analytical geometry, a convex polygon can be represented by the Cartesian coordinates of its vertices, x and y. Assume such data of a polygon are stored in a file called "vertices.dat". The first line contains an integer number, n, which denotes the total number of vertices/sides of the polygon. All the following lines should contain pairs of real numbers describing the coordinates of n points (one pair per line).
Create a Fortran program called "Polygon".
a- In the main program declare all necessary variables including n, an array for the abscissas (xdata) of the points, an array for the ordinates (y-data) of the points, etc. Assume a static size of 100 for arrays.
b- Write a subroutine which opens the input file "vertices.dat", reads n and the coordinates of the points from the input file.
c- Write a subroutine which calculates the length of all sides of the polygon.
d- Write a subroutine which calculates the perimeter of the polygon.
e- Write a subroutine that writes (using format descriptor "F") the length of all sides and the perimeter to an output file called "sides.dat" with 2 decimal places accuracy.
The main program calls in turn all the subroutines inside it. Type in the following data in "vertices.dat", run your program and find the length of all sides of the polygon and its perimeter.
Submit "sides.dat" with your report.