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Maximum area of quadrilateral
  • Difficulty Level : Medium
  • Last Updated : 15 Mar, 2021

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 quadilateral is given by K={\sqrt {(s-a)(s-b)(s-c)(s-d)-abcd\cdot \cos ^{2}\left({\frac {\alpha +\gamma }{2}}\right)}}
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\n",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.
?>

Javascript




<script>
 
// JavaScript program to find maximum are of a
// quadrilateral
 
function maxArea(a, b, c, d)
{
    // Calculating the semi-perimeter
    // of the given quadilateral
    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

 




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