The interior line is the sighting from the central point to the first corner, A. From there, the sightings are from A to B, from B to C, etc. and finally from E to A. The data in measures.txt are:
A surveyor has just completed surveying a parcel of land and wants to determine the parcel's area (in square feet). The surveyor started at a point near the center of the land, a place from which he could make a direct sighting of each of the corners of the parcel*. He took a sighting toward one corner and recorded the angle (relative to north) and the distance (in feet) to the corner. He then proceeded to go to that corner and take a sighting on the next corner going clockwise around the perimeter of the land. He recorded the angle and distance to the next corner and then proceeded to that corner to make the next sighting. He did this until he sighted the first corner again.
The surveyor put his measurements in a file; your program should prompt for the name of this file. For test purposes, you may use a file called measures1.txt; it has two trailing values of -1 to indicate the data is ended. Here is a sample of a parcel and the measurements that are in measures.txt; each line contains an angle and a distance (in that order). Note: all measured angles are relative to North. North is regarded as 0 o; East is 90o; South is 180o; and West is 270o. All distances are in feet.
The interior line is the sighting from
the central point to the first corner, A. From there, the sightings
are from A to B, from B to C, etc. and finally from E to A. The data
in measures.txt are:
309 186
111.5 194
177 140
253 190
30.5 164
324.5 153.9
-1 -1
Thus, from the central point to A is on a bearing of 309o for a distance of 186 feet and from A to B is on a bearing of 111.5o for 194 feet.
Write a program which can read such a file and display the area of the parcel in square feet, with one digit to the right of the decimal point. For this sample, area is 25216.3 sq ft. Note: parcels of land may have three or more sides.
*In general, not all parcels fit the criteria
of being able to directly sight each corner from some interior spot; however,
for purposes of this contest, all parcels used to test the program will
meet this criteria.