Program to find area of a polygon in Python

Suppose we have a list of ordered points represents a simple polygon endpoint on a 2D plane. We have to find the area of this polygon.

So, if the input is like points = [(0, 0), (0,5), (3, 5), (3,0)], then the output will be 15.

To solve this, we will follow these steps −

• Define a function getInfo() . This will take x1, y1, x2, y2
• return x1*y2 - y1*x2
• From the main method, do the following
• N := size of points
• (firstx, firsty) := points[0]
• (prevx, prevy) := (firstx, firsty)
• res := 0
• for i in range 1 to N-1, do
  • (nextx, nexty) := points[i]
  • res := res + getInfo(prevx, prevy, nextx, nexty)
  • prevx := nextx
  • prevy := nexty
• res := res + getInfo(prevx, prevy, firstx, firsty)
• return |res| / 2.0

Example

Let us see the following implementation to get better understanding −

def getInfo(x1, y1, x2, y2):
   return x1*y2 - y1*x2

def solve(points):
   N = len(points)
   firstx, firsty = points[0]
   prevx, prevy = firstx, firsty
   res = 0

   for i in range(1, N):
      nextx, nexty = points[i]
      res = res + getInfo(prevx,prevy,nextx,nexty)
      prevx = nextx
      prevy = nexty
   res = res + getInfo(prevx,prevy,firstx,firsty)
   return abs(res)/2.0

points = [(0, 0), (0,5), (3, 5), (3,0)]
print(solve(points))

Input

[(0, 0), (0,5), (3, 5), (3,0)]

Output

15.0