Maximum area of quadrilateral

Given four sides of quadrilateral a, b, c, d, find the maximum area of the quadrilateral possible from the given sides .

Examples:

Input : 1 2 1 2
Output : 2.00
It is optimal to construct a rectangle for maximum area .

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

According to Bretschneider’s formula, the area of a general quadilateral is given by $K={sqrt {(s-a)(s-b)(s-c)(s-d)-abcdcdot cos ^{2}left({frac {alpha +gamma }{2}} ight)}}$
Here a, b, c, d are the sides of a quadilateral, s is the semiperimeter of a quadilateral and angles are two opposite angles.
So, this formula is maximized only when opposite angles sum to pi(180) then we can use a simplified form of Bretschneider’s formula to get the (maximum) area K.
$K={sqrt {(s-a)(s-b)(s-c)(s-d)}}$

This formula is called as Brahmagupta’s formula .

Below is the implementation of given approach

C++

// CPP program to find maximum are of a  
// quadrilateral 
#include <bits/stdc++.h> 
using namespace std; 
  
double maxArea(double a, double b, 
                double c, double d) 
{ 
    // Calculating the semi-perimeter  
    // of the given quadilateral 
    double semiperimeter = (a + b + c + d) / 2; 
  
    // Applying Brahmagupta's formula to 
    // get maximum area of quadrilateral 
    return sqrt((semiperimeter - a) * 
                (semiperimeter - b) *  
                (semiperimeter - c) *  
                (semiperimeter - d)); 
} 
  
// Driver code 
int main() 
{ 
    double a = 1, b = 2, c= 1, d = 2; 
    printf("%.2f
",maxArea(a, b, c, d)); 
    return 0; 
}

Java

// Java program to find maximum are of a  
// quadrilateral 
import java.io.*; 
  
class GFG  
{ 
    static double maxArea(double a, double b, 
                           double c, double d) 
    { 
        // Calculating the semi-perimeter  
        // of the given quadilateral 
        double semiperimeter = (a + b + c + d) / 2; 
      
        // Applying Brahmagupta's formula to 
        // get maximum area of quadrilateral 
        return Math.sqrt((semiperimeter - a) * 
                         (semiperimeter - b) *  
                         (semiperimeter - c) *  
                         (semiperimeter - d)); 
    } 
      
    // Driver code 
    public static void main (String[] args)  
    { 
        double a = 1, b = 2, c= 1, d = 2; 
        System.out.println(maxArea(a, b, c, d)); 
    } 
} 
  
// This code is contributed by sunnysingh 

Python3

# Python3 program to find maximum  
# area of a quadrilateral 
import math 
  
def maxArea (a , b , c , d ): 
  
    # Calculating the semi-perimeter 
    # of the given quadilateral 
    semiperimeter = (a + b + c + d) / 2
      
    # Applying Brahmagupta's formula to 
    # get maximum area of quadrilateral 
    return math.sqrt((semiperimeter - a) *
                    (semiperimeter - b) *
                    (semiperimeter - c) * 
                    (semiperimeter - d)) 
  
# Driver code 
a = 1
b = 2
c = 1
d = 2
print("%.2f"%maxArea(a, b, c, d)) 
  
# This code is contributed by "Sharad_Bhardwaj". 

C#

// C# program to find maximum are of a  
// quadrilateral 
using System; 
  
class GFG { 
      
    static double maxArea(double a, double b, 
                          double c, double d) 
    { 
          
        // Calculating the semi-perimeter  
        // of the given quadilateral 
        double semiperimeter = (a + b + c + d) / 2; 
      
        // Applying Brahmagupta's formula to 
        // get maximum area of quadrilateral 
        return Math.Sqrt((semiperimeter - a) * 
                         (semiperimeter - b) *  
                         (semiperimeter - c) *  
                         (semiperimeter - d)); 
    } 
      
    // Driver code 
    public static void Main ()  
    { 
        double a = 1, b = 2, c= 1, d = 2; 
          
        Console.WriteLine(maxArea(a, b, c, d)); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP program to find maximum are of a  
// quadrilateral 
  
function maxArea( $a, $b, $c, $d) 
{ 
      
    // Calculating the semi-perimeter  
    // of the given quadilateral 
    $semiperimeter = ($a + $b + $c + $d) / 2; 
  
    // Applying Brahmagupta's formula to 
    // get maximum area of quadrilateral 
    return sqrt(($semiperimeter - $a) * 
                ($semiperimeter - $b) *  
                ($semiperimeter - $c) *  
                ($semiperimeter - $d)); 
} 
  
// Driver code 
$a = 1; $b = 2; $c= 1; $d = 2; 
echo(maxArea($a, $b, $c, $d)); 
  
// This code is contributed by vt_m. 
?> 

Output:

2.00

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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