Green's Theorem Area

Problem

Green's theorem gives the area enclosed by a simple closed curve as A = 0.5 * |closed integral of (x dy - y dx)|.

For a polygon given by its vertices in order, this becomes the shoelace formula 0.5 * |sum of (x_i * y_{i+1} - x_{i+1} * y_i)|. Return 0.0 for fewer than 3 vertices.

Hint

The edge from the last vertex back to the first closes the loop.

Test cases

case 1

in: [[[0,0],[1,0],[1,1],[0,1]]]

expected: 1

case 2

in: [[[0,0],[2,0],[0,2]]]

expected: 2

case 3

in: [[[0,0]]]

expected: 0

case 4

in: [[[0,0],[4,0],[4,3]]]

expected: 6

case 5

in: [[[1,1],[3,1],[3,2],[1,2]]]

expected: 2

Starter codePython

def polygon_area(vertices):
    # vertices is a list of [x, y] pairs in order
    # Your code here
    pass

5 test cases · run your code against them in the editor