ESc101 Laboratory Assignment
                       Tuesday of week of 13/9/04

Area of a five-sided Polygon
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Write a program which takes as input the points of a
five-sided polygon, P1:(x1,y1), P2:(x2.y2), P3:(x3,y3),
P4:(x4,y4), P5:(x5,y5) which are successive points on the 
polygon, i.e., P1P2 is an edge, P2P3 is an edge and so on.

It finds out whether the polygon is simple (i.e. no two
non-adjacent edges intersect or touch each other) and if it is 
simple, then computes the area of the polygon. You may assume 
that if the polynomial is simple, then points are given in 
anti-clockwise order. Print the result.

Observe that there are four types of simple 5-sided polygons:
with no concave angle (inside angle >= 180 degrees), 
with one concave angle, with two adjacent concave angles and 
with two non-adjacent concave angles. The area can be computed 
by suitably splitting the polygon into three triangles. To
decide whether angle Pi-1 Pi Pi+1 is concave or convex, find out 
whether from segment Pi-1Pi to segment PiPi+1 is a right-turn
or a left turn (the interior is on the left side). Use vector 
cross product to find the nature of the turn.

Carefully design your solution to avoid explosion of the cases.

NOTE; DO NOT USE LOOPS, ARRAYS, OR VECTORS.