# Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle

• Last Updated : 07 Aug, 2022

Given here is an equilateral triangle of sidelength a which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Examples:

Input : a = 5
Output : 3.79335

Input : a = 9
Output : 12.2905

Approach: We know that the side of the square inscribed within an equilateral triangle of side length is, x = 0.464*a (Please refer here).
Also, in the reuleaux triangle, h = x.
So, Area of Reuleaux Triangle

A = 0.70477*h2
= 0.70477*(0.464*a)2

Below is the implementation of the above approach:

## C++

 // C++ Program to find the biggest Reuleaux triangle// inscribed within in a square which in turn// is inscribed within an equilateral triangle#include using namespace std; // Function to find the biggest reuleaux trianglefloat Area(float a){     // side cannot be negative    if (a < 0)        return -1;     // height of the reuleaux triangle    float x = 0.464 * a;     // area of the reuleaux triangle    float A = 0.70477 * pow(x, 2);     return A;} // Driver codeint main(){    float a = 5;    cout << Area(a) << endl;     return 0;}

## Java

 // Java Program to find the biggest Reuleaux triangle// inscribed within in a square which in turn// is inscribed within an equilateral triangle class GFG{     // Function to find the biggest reuleaux trianglestatic float Area(float a){     // side cannot be negative    if (a < 0)        return -1;     // height of the reuleaux triangle    float x = 0.464f * a;     // area of the reuleaux triangle    float A = 0.70477f * (float)Math.pow(x, 2);     return A;} // Driver codepublic static void main (String[] args){    float a = 5;    System.out.println(String.format("%.5f", Area(a)));}} // This code is contributed by chandan_jnu

## Python3

 # Python3 Program to find the biggest# Reuleaux triangle inscribed within# in a square which in turn is inscribed# within an equilateral triangleimport math as mt # Function to find the biggest# reuleaux triangledef Area(a):     # side cannot be negative    if (a < 0):        return -1     # height of the reuleaux triangle    x = 0.464 * a     # area of the reuleaux triangle    A = 0.70477 * pow(x, 2)     return A # Driver codea = 5print(Area(a)) # This code is contributed by# Mohit Kumar 29

## C#

 // C# Program to find the biggest Reuleaux// triangle inscribed within in a square// which in turn is inscribed within an// equilateral triangleusing System; class GFG{     // Function to find the biggest// reuleaux trianglestatic float Area(float a){     // side cannot be negative    if (a < 0)        return -1;     // height of the reuleaux triangle    float x = 0.464f * a;     // area of the reuleaux triangle    float A = 0.70477f * (float)Math.Pow(x, 2);     return A;} // Driver codepublic static void Main (){    float a = 5;    Console.WriteLine(String.Format("{0,0:#.00000}",                                          Area(a)));}} // This code is contributed by Akanksha Rai



## Javascript



Output:

3.79335

Time complexity: O(1)

Auxiliary Space: O(1)

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