正方形的外接圆面积

给定一个正方形的边，然后找到它周围的外接圆的面积。
例子：

Input : a = 6
Output : Area of a circumscribed circle is : 56.55

Input : a = 4
Output : Area of a circumscribed circle is : 25.13

正方形的四个边长相等，四个角都是90度。该圆外接在给定的正方形上，由下图中的阴影区域显示。

外切圆的性质如下：

• 外接圆的中心是正方形的两条对角线相交的点。
• 正方形的外接圆是由正方形的四个顶点构成的。
• 正方形外接圆的半径等于正方形的半径。

Formula used to calculate the area of inscribed circle is: 
(PI * a * a)/2 
where, a is the side of a square in which a circle is circumscribed.
How does this formula work? 
We know area of circle = PI*r*r. 
We also know radius of circle = (square diagonal)/2 
Length of diagonal = ?(2*a*a) 
Radius = ?(2*a*a)/2 = ?((a*a)/2) 
Area = PI*r*r = (PI*a*a)/2

C++

// C++ Program to find the
// area of a circumscribed circle
#include 
#define PI 3.14159265
 
float areacircumscribed(float a)
{
    return (a * a * (PI / 2));
}
 
// Driver code
int main()
{
    float a = 6;
    printf(" Area of an circumscribed circle is : %.2f ",
           areacircumscribed(a));
    return 0;
}

Java

// Java program to calculate
// area of a circumscribed circle-square
import java.io.*;
class Gfg {
    // Utility Function
    static float areacircumscribed(float a)
    {
        float PI = 3.14159265f;
        return (a * a * (PI / 2));
    }
 
    // Driver Function
    public static void main(String arg[])
    {
        float a = 6;
        System.out.print("Area of an circumscribed"
                         + "circle is :");
        System.out.println(areacircumscribed(a));
    }
}
 
// The code is contributed by Anant Agarwal.

Python3

# Python3 Program to find the
# area of a circumscribed circle
PI = 3.14159265
 
def areacircumscribed(a):
 
    return (a * a * (PI / 2))
 
# Driver code
a = 6
print(" Area of an circumscribed circle is :",
        round(areacircumscribed(a), 2))
         
# This code is contributed by Smitha Dinesh Semwal

C#

// C# Program to find the
// area of a circumscribed circle
using System;
 
class GFG {
     
    public static double PI= 3.14159265 ;
 
    static float areacircumscribed(float a)
    {
        return (a * a * (float)(PI / 2));
    }
     
    // Driver code
    public static void Main()
    {
        float a = 6;
         
        Console.Write(" Area of an circumscribed"
                            + " circle is : {0}",
             Math.Round(areacircumscribed(a), 2));
    }
}
 
// This code is contributed by
// Smitha Dinesh Semwal

Javascript

 
// Javascript Program to find the
// area of a circumscribed circle
function areacircumscribed(a)
{
    return (a * a * (3.1415 / 2));
}
 
// Driver code
    let a = 6;
    document.write(" Area of an circumscribed circle is : ",
        areacircumscribed(a));
 
// This code is contributed by Mayank Tyagi

输出 ：

Area of an circumscribed circle is : 56.55