Saturday, 23 Oct 2021

# Calculate area of a cyclic quadrilateral with given side lengths

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 = 25Output: 273.861Input: A = 10, B = 30, C = 50, D = 20Output: 443.706Approach: 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 circum-circle or circumscribed circle, and the vertices are said to be concyclic. In the above image above r is the radius of the circum-circle 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 andα and γ 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 sqrt(s – A)*(s – B)*(s – C)*(s – D) .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++  #include using namespace std;  float calculateArea(float A, float B,                    float C, float D){            float S = (A + B + C + D) / 2;          float area = sqrt((S – A) * (S – B)                      * (S – C) * (S – D));          return area;}  int main(){    float A = 10;    float B = 15;    float C = 20;    float D = 25;    cout