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Area of a square inscribed in a circle which is inscribed in an equilateral triangle

  • Last Updated : 15 Mar, 2021

Given here is an equilateral triangle with side length a, which inscribes a circle, which in turn inscribes a square. The task is to find the area of this square.
Examples: 
 

Input: a = 6
Output: 1

Input: a = 10
Output: 0.527046

 

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Approach:
 

let r be the radius of circle, 
hence it is the inradius of equilateral triangle, so r = a /(2 * √3) 
diagonal of square, d = diameter of circle = 2 * r = a/ √3 
So, area of square, A = 0.5 * d * d 
hence A = (1/2) * (a^2) / (3) = (a^2/6)

Below is the implementation of the above approach: 
 

C++




// C++ Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in an equilateral triangle
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area of the square
float area(float a)
{
 
    // a cannot be negative
    if (a < 0)
        return -1;
 
    // area of the square
    float area = sqrt(a) / 6;
 
    return area;
}
 
// Driver code
int main()
{
    float a = 10;
    cout << area(a) << endl;
    return 0;
}

Java




// Java Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in an equilateral triangle
 
import java.io.*;
 
class GFG {
    
 
// Function to find the area of the square
static float area(float a)
{
 
    // a cannot be negative
    if (a < 0)
        return -1;
 
    // area of the square
    float area = (float)Math.sqrt(a) / 6;
 
    return area;
}
 
// Driver code
    public static void main (String[] args) {
        float a = 10;
    System.out.println( area(a));
// This code is contributed
// by  inder_verma..
    }
}

Python 3




# Python3 Program to find the area
# of the square inscribed within 
# the circle which in turn is
# inscribed in an equilateral triangle
 
# import everything from math lib.
from math import *
 
# Function to find the area
# of the square
def area(a):
 
    # a cannot be negative
    if a < 0 :
        return -1
 
    # area of the square
    area = sqrt(a) / 6
 
    return area
 
# Driver code    
if __name__ == "__main__" :
 
    a = 10
    print(round(area(a), 6))
 
# This code is contributed by ANKITRAI1

C#




// C# Program to find the area
// of the square inscribed within
// the circle which in turn is
// inscribed in an equilateral triangle
using System;
 
class GFG
{
     
// Function to find the area
// of the square
static float area(float a)
{
 
    // a cannot be negative
    if (a < 0)
        return -1;
 
    // area of the square
    float area = (float)Math.Sqrt(a) / 6;
 
    return area;
}
 
// Driver code
public static void Main ()
{
    float a = 10;
    Console.WriteLine(area(a));
}
}
 
// This code is contributed
// by inder_verma

PHP




<?php
// PHP Program to find the area
// of the square inscribed within
// the circle which in turn is
// inscribed in an equilateral triangle
 
// Function to find the
// area of the square
function area($a)
{
 
    // a cannot be negative
    if ($a < 0)
        return -1;
 
    // area of the square
    $area = sqrt($a) / 6;
 
    return $area;
}
 
// Driver code
$a = 10;
echo area($a);
 
// This code is contributed
// by inder_verma
?>

Javascript




<script>
// javascript Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in an equilateral triangle
 
 
// Function to find the area of the square
function area(a)
{
 
    // a cannot be negative
    if (a < 0)
        return -1;
 
    // area of the square
    var area = Math.sqrt(a) / 6;
 
    return area;
}
 
// Driver code
var a = 10;
document.write( area(a).toFixed(6));
 
 
// This code contributed by shikhasingrajput
 
</script>
Output: 
0.527046

 




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