Given four positive integers A, B, C, and D representing the length of sides of a Cyclic Quadrilateral, the task is to find the area of the Cyclic Quadrilateral.
Examples:
Input: A = 10, B = 15, C = 20, D = 25
Output: 273.861Input: A = 10, B = 30, C = 50, D = 20
Output: 443.706
Approach: The given problem can be solved based on the following observations:
- A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
- In the above image above r is the radius of the circumcircle and A, B, C, and D are the lengths of the sides PQ, QR, RS, and SP respectively.
- The area of the quadrilateral is given by Bretschneider’s formula is:
where, A, B, C, and D are the sides of the triangle and
? and ? are the opposite angles of the quadrilateral.Since, the sum of opposite angles of the quadrilateral is 180 degree. Therefore, the value of cos(180/2) = cos(90) = 0.
Therefore, the formula for finding the area reduces to
.
Therefore, the idea is to print the value of 
as the resultant area of the given quadrilateral.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the area// of cyclic quadrilateralfloat calculateArea(float A, float B, float C, float D){ // Stores the value of // half of the perimeter float S = (A + B + C + D) / 2; // Stores area of cyclic quadrilateral float area = sqrt((S - A) * (S - B) * (S - C) * (S - D)); // Return the resultant area return area;}// Driver Codeint main(){ float A = 10; float B = 15; float C = 20; float D = 25; cout << calculateArea(A, B, C, D); return 0;} |
Java
// Java program for the above approachimport java.io.*;class GFG{ // Function to find the area// of cyclic quadrilateralstatic float calculateArea(float A, float B, float C, float D){ // Stores the value of // half of the perimeter float S = (A + B + C + D) / 2; // Stores area of cyclic quadrilateral float area = (float)Math.sqrt((S - A) * (S - B) * (S - C) * (S - D)); // Return the resultant area return area;}// Driver codepublic static void main (String[] args){ float A = 10; float B = 15; float C = 20; float D = 25; System.out.println(calculateArea(A, B, C, D));}}// This code is contributed by Ankita saini |
Python3
# Python3 program for the above approachfrom math import sqrt# Function to find the area# of cyclic quadrilateraldef calculateArea(A, B, C, D): # Stores the value of # half of the perimeter S = (A + B + C + D) // 2 # Stores area of cyclic quadrilateral area = sqrt((S - A) * (S - B) * (S - C) * (S - D)) # Return the resultant area return area# Driver Codeif __name__ == '__main__': A = 10 B = 15 C = 20 D = 25 print(round(calculateArea(A, B, C, D), 3))# This code is contributed by mohit kumar 29 |
C#
// C# program for the above approachusing System;class GFG{// Function to find the area// of cyclic quadrilateralstatic float calculateArea(float A, float B, float C, float D){ // Stores the value of // half of the perimeter float S = (A + B + C + D) / 2; // Stores area of cyclic quadrilateral float area = (float)Math.Sqrt((S - A) * (S - B) * (S - C) * (S - D)); // Return the resultant area return area;}// Driver Codestatic public void Main(){ float A = 10; float B = 15; float C = 20; float D = 25; Console.Write(calculateArea(A, B, C, D));}}// This code is contributed by code_hunt |
Javascript
<script>// java script program for the above approach// Function to find the area//of cyclic quadrilateralfunction calculateArea(A, B, C, D){ //Stores the value of // half of the perimeter let S = (A + B + C + D) /2 // Stores area of cyclic quadrilateral let area = Math.sqrt((S - A) * (S - B) * (S - C) * (S - D)) //Return the resultant area return area; }// Driver Code let A = 10; let B = 15; let C = 20; let D = 25; document.write(calculateArea(A, B, C, D).toFixed(3))//this code is contributed by sravan kumar</script> |
Output:
273.861
Time Complexity: O(1)
Auxiliary Space: O(1)
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