Calculating Area Around a Path

[rowardHoark]

http://img838.imageshack.us/img838/1538/physicsforumquestion.png

Say "A" is a river. It is a linear approximation because only several coordinate points are known. The total length is "l" (obtained from the coordinates), "a" represents the distance from the river at which the soil is fertile.

The goal is to obtain the total fertile area. If $Area=l*a$ the result is very inaccurate for small angles between lines, as an extra, overlapping, area (represented as red in "B") is added.

How could I obtain a more accurate value?

 

[HallsofIvy]

Well, you know how to find the area of triangles, don't you? Your area can be reduced to a series of rectantgles with the area of triangles, where they overlap, subtracted off.

 

[rowardHoark]

Thank you, HallsofIvy. I will try to incorporate angles into my mathematical model. I know the coordinates of the points where the lines meet, hence can derive angles.

The system is dynamic. The coordinate points are generated randomly, therefore I need to be able to know the exact area for various arrangements, and it has to be done automatically using an algorithm.