Given four sides of a quadrilateral, the task is to get the maximum area of the given quadrilateral for the given four sides in python.

**Quadrilateral:**

In geometry, a quadrilateral is a closed shape formed by joining four points, any three of which are non-collinear. A quadrilateral is made up of four sides, four angles, and four vertices. The term ‘quadrilateral’ is derived from the Latin words ‘quadra’ (four) and ‘Latus’ (sides). A quadrilateral’s four sides may or may not be equal.

Formula:The formula to calculate the maximum area of the given quadrilateral is :

This is known as Brahmagupta’s Formula.

s=(a+b+c+d)/2where a, b, c, d are the four sides of a quadrilateral.

**Examples:**

**Example1:**

**Input:**

Given first side = 2 Given second side = 1 Given third side = 3 Given fourth side = 4

**Output:**

The maximimum area of quadrilateral for the given four sides { 2 , 1 , 3 , 4 } = 4.898979485566356

**Example2:**

**Input:**

Given first side = 5 Given second side = 3 Given third side = 5 Given fourth side = 2

**Output:**

The maximimum area of quadrilateral for the given four sides { 5 , 3 , 5 , 2 } = 12.43734296383275

## Program for Maximum Area of Quadrilateral in Python

Below are the ways to get the maximum area of the given quadrilateral for the given four sides in python:

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

**Approach:**

- Import math module using the import keyword.
- Give the first side as static input and store it in a variable.
- Give the second side as static input and store it in another variable.
- Give the third side as static input and store it in another variable.
- Give the fourth side as static input and store it in another variable.
- Calculate the s value using the above given mathematical formula and store it in another variable.
- Calculate the maximum area of the given quadrilateral using the above given mathematical formula, math.sqrt() function and store it in another variable.
- Print the maximum area of the given quadrilateral.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Give the first side as static input and store it in a variable. p = 2 # Give the second side as static input and store it in another variable. q = 1 # Give the third side as static input and store it in another variable. r = 3 # Give the fourth side as static input and store it in another variable. s = 4 # Calculate the s value using the above given mathematical formula and # store it in another variable. s_valu = (p + q + r + s) / 2 # Calculate the maximum area of the given quadrilateral using the above # given mathematical formula, math.sqrt() function and store it in another variable. quadriltrlmax_area = math.sqrt( (s_valu - p) * (s_valu - q) * (s_valu - r) * (s_valu - s)) # Print the maximum area of the given quadrilateral. print( "The maximimum area of quadrilateral for the given four sides {", p, ",", q, ",", r, ",", s, "} = ", quadriltrlmax_area)

# include <iostream> # include<cmath> using namespace std int main() { int p = 2 int q = 1 int r = 3 int s = 4 int s_valu = (p + q + r + s) / 2 double quadriltrlMaxArea = sqrt((s_valu - p) * (s_valu - q) * (s_valu - r) * (s_valu - s)) cout << "The maximimum area of quadrilateral for the given four sides {" << p << "," << q << "," << r << "," << s << "} = " << quadriltrlMaxArea << endl return 0 }

**Output:**

The maximimum area of quadrilateral for the given four sides { 2 , 1 , 3 , 4 } = 4.898979485566356

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

**Approach:**

- Import math module using the import keyword.
- Give the first side as user input using the int(input()) function and store it in a variable.
- Give the second side as user input using the int(input()) function and store it in another variable.
- Give the third side as user input using the int(input()) function and store it in another variable.
- Give the fourth side as user input using the int(input()) function and store it in another variable.
- Calculate the s value using the above given mathematical formula and store it in another variable.
- Calculate the maximum area of the given quadrilateral using the above given mathematical formula, math.sqrt() function and store it in another variable.
- Print the maximum area of the given quadrilateral.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Give the first side as user input using the int(input()) function and store it in a variable. p = int(input("Enter some random number = ")) # Give the second side as user input using the int(input()) function and store it in another variable. q = int(input("Enter some random number = ")) # Give the third side as user input using the int(input()) function and store it in another variable. r = int(input("Enter some random number = ")) # Give the fourth side as user input using the int(input()) function and store it in another variable. s = int(input("Enter some random number = ")) # Calculate the s value using the above given mathematical formula and # store it in another variable. s_valu = (p + q + r + s) / 2 # Calculate the maximum area of the given quadrilateral using the above # given mathematical formula, math.sqrt() function and store it in another variable. quadriltrlmax_area = math.sqrt( (s_valu - p) * (s_valu - q) * (s_valu - r) * (s_valu - s)) # Print the maximum area of the given quadrilateral. print( "The maximimum area of quadrilateral for the given four sides {", p, ",", q, ",", r, ",", s, "} = ", quadriltrlmax_area)

**Output:**

Enter some random number = 5 Enter some random number = 3 Enter some random number = 5 Enter some random number = 2 The maximimum area of quadrilateral for the given four sides { 5 , 3 , 5 , 2 } = 12.43734296383275

**Output:**