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
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 squarefloat area(float a){ // a cannot be negative if (a < 0) return -1; // area of the square float area = sqrt(a) / 6; return area;}// Driver codeint 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 triangleimport java.io.*;class GFG { // Function to find the area of the squarestatic 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 triangleusing System;class GFG { // Function to find the area // of the squarestatic 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 codepublic 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 squarefunction 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 squarefunction area(a){ // a cannot be negative if (a < 0) return -1; // area of the square var area = Math.sqrt(a) / 6; return area;}// Driver codevar a = 10;document.write( area(a).toFixed(6));// This code contributed by shikhasingrajput </script> |
Output:
0.527046
Time complexity : O(log(a)) for given side a, as complexity of inbuilt sqrt function
Auxiliary Space : O(1)
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