Maximum area of quadrilateral

Difficulty Level : Easy
Last Updated : 22 Jun, 2022

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 $K={\sqrt {(s-a)(s-b)(s-c)(s-d)-abcd\cdot \cos ^{2}\left({\frac {\alpha +\gamma }{2}}\right)}}$
Here a, b, c, d are the sides of a 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.
$K={\sqrt {(s-a)(s-b)(s-c)(s-d)}}$
This formula is called as Brahmagupta’s formula .
Below is the implementation of given approach

C++

// CPP program to find maximum 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

My Personal Notes

May	JUN	Jul
	29
2021	2022	2023

Related Articles

Maximum area of quadrilateral

C++

C

Java

Python3

C#

PHP

Javascript

Start Your Coding Journey Now!