Given two lists which are the ordered coordinates of a polygon with n vertices, the task is to find the area of a given polygon.

Ordered means that the coordinates are given either clockwise or anticlockwise from the first vertex to the last.

**Examples:**

**Example1:**

**Input:**

Given x-coordinates list = [1, 5, 1] Given y-coordinates list = [6, 4, 3]

**Output:**

The Area of the given polygon for the given n ordered vertices : 6

**Example2:**

**Input:**

Given x-coordinates list = [2, 3, 3, 1] Given y-coordinates list = [9, 2, 1, 2]

**Output:**

The Area of the given polygon for the given n ordered vertices : 8

## Program for Area of a Polygon with Given n Ordered Vertices in Python

Below are the ways to find the area of a given polygon for the given n ordered vertices in python:

### Method #1: Using Mathematical Formula (Static Input)

**Approach:**

- Give the x-coordinates list as static input and store it in a variable.
- Give the y-coordinates list as static input and store it in another variable.
- Calculate the length of the given x-coordinates list and store it in another variable.
- Take a variable say
**polygn_area**and initialize its value to 0. - Subtract 1 from the above x-coordinates list length and store it in another variable say k .
- Loop till the length of the given x-coordinates list using the for loop.
- Calculate the area of the polygon using the above given mathematical formula and add it to the above-initialized variable
**polygn_areaÂ** - Assign the value of the iterator to the k which is the previous vertex to the iterator.
- Divide the above
**polygn_area**by 2, apply the abs() function to it which gives the absolute value, and convert it to an integer using the int() function. - Store it in another variable.
- Print the above result which is the area of the given polygon.
- The Exit of the Program.

**Below is the implementation:**

# Give the x-coordinates list as static input and store it in a variable. a = [1, 5, 1] # Give the y-coordinates list as static input and store it in another variable. b = [6, 4, 3] # Calculate the length of the given x-coordinates list and store it in another variable. lst_lengt = len(a) # Take a variable say polygn_area and initialize its value to 0. polygn_area = 0 # Subtract 1 from the above x-coordinates list length and store it in another variable # say k . k = lst_lengt - 1 print("The Area of the given polygon for the given n ordered vertices :") # Loop till the length of the given x-coordinates list using the for loop. for itr in range(0, lst_lengt): # Calculate the area of the polygon using the above given mathematical formula and # add it to the above-initialized variable polygn_area. polygn_area += (a[k] + a[itr]) * (b[k] - b[itr]) # Assign the value of the iterator to the k which is the previous vertex # to the iterator. k = itr # Divide the above polygn_area by 2, apply the abs() function to it which gives # the absolute value, and convert it to an integer using the int() function. # Store it in another variable. rslt = int(abs(polygn_area / 2.0)) # Print the above result which is the area of the given polygon. print(rslt)

**Output:**

The Area of the given polygon for the given n ordered vertices : 6

### Method #2: Using Mathematical Formula (User Input)

**Approach:**

- Give the x-coordinates list as user input using list(),map(),input(),and split() functions.
- Store it in a variable.
- Give the y-coordinates list as user input using list(),map(),input(),and split() functions.
- Store it in another variable.
- Calculate the length of the given x-coordinates list and store it in another variable.
- Take a variable say
**polygn_area**and initialize its value to 0. - Subtract 1 from the above x-coordinates list length and store it in another variable say k .
- Loop till the length of the given x-coordinates list using the for loop.
- Calculate the area of the polygon using the above given mathematical formula and add it to the above-initialized variable
**polygn_areaÂ** - Assign the value of the iterator to the k which is the previous vertex to the iterator.
- Divide the above
**polygn_area**by 2, apply the abs() function to it which gives the absolute value, and convert it to an integer using the int() function. - Store it in another variable.
- Print the above result which is the area of the given polygon.
- The Exit of the Program.

**Below is the implementation:**

# Give the x-coordinates list as user input using list(),map(),input(),and split() functions. # Store it in a variable. a = list(map(int, input( 'Enter some random List Elements separated by spaces = ').split())) # Give the y-coordinates list as user input using list(),map(),input(),and split() functions. # Store it in another variable. b = list(map(int, input( 'Enter some random List Elements separated by spaces = ').split())) # Calculate the length of the given x-coordinates list and store it in another variable. lst_lengt = len(a) # Take a variable say polygn_area and initialize its value to 0. polygn_area = 0 # Subtract 1 from the above x-coordinates list length and store it in another variable # say k . k = lst_lengt - 1 print("The Area of the given polygon for the given n ordered vertices :") # Loop till the length of the given x-coordinates list using the for loop. for itr in range(0, lst_lengt): # Calculate the area of the polygon using the above given mathematical formula and # add it to the above-initialized variable polygn_area. polygn_area += (a[k] + a[itr]) * (b[k] - b[itr]) # Assign the value of the iterator to the k which is the previous vertex # to the iterator. k = itr # Divide the above polygn_area by 2, apply the abs() function to it which gives # the absolute value, and convert it to an integer using the int() function. # Store it in another variable. rslt = int(abs(polygn_area / 2.0)) # Print the above result which is the area of the given polygon. print(rslt)

**Output:**

Enter some random List Elements separated by spaces = 2 3 3 1 Enter some random List Elements separated by spaces = 9 2 1 2 The Area of the given polygon for the given n ordered vertices : 8