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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 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


This article is attributed to GeeksforGeeks.org

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