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.
Contact Us