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 .

According to Bretschneider’s formula, the area of a general quadrilateral is given by 
Here a, b, c, d are the sides of a quadrilateral, s is the semiperimeter of a quadrilateral 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. 

This formula is called as Brahmagupta’s formula . 
Below is the implementation of given approach

C++

// CPP program to find maximum area of a
// quadrilateral
#include <iostream>
#include <math.h>
using namespace std;

double maxArea(double a, double b,
                double c, double d)
{
    // Calculating the semi-perimeter
    // of the given quadrilateral
    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;
   cout <<maxArea(a, b, c, d);
    return 0;
}

// This code is contributed by shivanisinghss2110

C

// CPP program to find maximum area of a
// quadrilateral
#include <stdio.h>
#include <math.h>

double maxArea(double a, double b,
                double c, double d)
{
    // Calculating the semi-perimeter
    // of the given quadrilateral
    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\n",maxArea(a, b, c, d));
    return 0;
}

Java

// Java program to find maximum area 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 quadrilateral
        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 quadrilateral
    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 area 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 quadrilateral
        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 area of a
// quadrilateral

function maxArea( $a, $b, $c, $d)
{

    // Calculating the semi-perimeter
    // of the given quadrilateral
    $semiperimeter = ($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.
?>

Javascript

<script>

// JavaScript program to find maximum area of a
// quadrilateral

function maxArea(a, b, c, d)
{
    // Calculating the semi-perimeter
    // of the given quadrilateral
    let 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

    let a = 1, b = 2, c= 1, d = 2;
    document.write(maxArea(a, b, c, d));

// This code is contributed by Surbhi Tyagi.

</script>

Output: 

2.00

Time Complexity: O(logn) 
Auxiliary Space: O(1)

Please suggest if someone has a better solution which is more efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above