Python: Compute the area of the polygon

Last update on April 17 2025 13:01:24 (UTC/GMT +8 hours)

Convex Polygon Area

A convex polygon is a simple polygon in which no line segment between two points on the boundary ever goes outside the polygon. Equivalently, it is a simple polygon whose interior is a convex set. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees.

Write a Python program that compute the area of the polygon . The vertices have the names vertex 1, vertex 2, vertex 3, ... vertex n according to the order of edge connections.

Input:
Input number of sides: 5
Side: 1
Input the Coordinate:
Input Coordinate x: 1
Input Coordinate y: 0
Side: 2
Input the Coordinate:
Input Coordinate x: 0
Input Coordinate y: 0
Side: 3
Input the Coordinate:
Input Coordinate x: 1
Input Coordinate y: 1
Side: 4
Input the Coordinate:
Input Coordinate x: 2
Input Coordinate y: 0
Side: 5
Input the Coordinate:
Input Coordinate x: -1
Input Coordinate y: 1
Area of the Polygon: 0.5

Visual Presentation:

Sample Solution:

Python Code:

# Define a function 'poly_area' to calculate the area of a polygon
def poly_area(c):
    # Initialize an empty list 'add' to store intermediate values
    add = []
    
    # Use a loop to iterate through the coordinates
    for i in range(0, (len(c) - 2), 2):
        # Calculate and append the cross product of consecutive coordinate pairs
        add.append(c[i] * c[i + 3] - c[i + 1] * c[i + 2])
    
    # Calculate and append the cross product of the last and first coordinate pairs
    add.append(c[len(c) - 2] * c[1] - c[len(c) - 1] * c[0])
    
    # Return the absolute value of half of the sum of all cross products
    return abs(sum(add) / 2)

# Prompt the user to input the number of sides of the polygon
no_sides = int(input('Input number of sides: '))
# Initialize an empty list 'cord_data' to store coordinates
cord_data = []

# Use a loop to input coordinates for each side of the polygon
for z in range(no_sides):
    print("Side:", z+1)
    print("Input the Coordinate:")
    # Input x-coordinate
    x = int(input('Input Coordinate x:'))
    # Input y-coordinate
    y = int(input('Input Coordinate y:'))
    # Append the coordinates to 'cord_data'
    cord_data.append(x)
    cord_data.append(y)

# Print the area of the polygon using the 'poly_area' function
print("\nArea of the Polygon:", poly_area(cord_data))

Sample Output:

Input number of sides:  5
Side: 1
Input the Coordinate:
Input Coordinate x: 1
Input Coordinate y: 0
Side: 2
Input the Coordinate:
Input Coordinate x: 0
Input Coordinate y: 0
Side: 3
Input the Coordinate:
Input Coordinate x: 1
Input Coordinate y: 1
Side: 4
Input the Coordinate:
Input Coordinate x: 2
Input Coordinate y: 0
Side: 5
Input the Coordinate:
Input Coordinate x: -1
Input Coordinate y: 1

Area of the Polygon: 0.5

Explanation:

Here is a breakdown of the above Python code:

• Define a function "poly_area()" to calculate the area of a polygon using the shoelace formula.
• Initialize an empty list 'add' to store intermediate values.
• Use a loop to calculate and append the cross product of consecutive coordinate pairs.
• Calculate and append the cross product of the last and first coordinate pairs.
• Return the absolute value of half of the sum of all cross products.
• Prompt the user to input the number of sides of the polygon.
• Initialize an empty list 'cord_data' to store coordinates.
• Use a loop to input coordinates for each side of the polygon.
• Print the area of the polygon using the "poly_area()" function.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to calculate the area of a convex polygon given its vertices using the shoelace formula.
• Write a Python program to compute the area of a convex polygon after ensuring that the vertex list is correctly ordered.
• Write a Python program to sort unordered vertices of a convex polygon and then calculate its area.
• Write a Python program to triangulate a convex polygon and sum the areas of the constituent triangles to find the total area.

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