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 <bits/stdc++.h> using namespace std; // Function to find the biggest reuleaux triangle float 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 code int main() { float a = 5; cout << Area(a) << endl; return 0; } |
chevron_right
filter_none
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 triangle static 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 code public static void main (String[] args) { float a = 5; System.out.println(String.format("%.5f", Area(a))); } } // This code is contributed by chandan_jnu |
chevron_right
filter_none
Python3
# Python3 Program to find the biggest # Reuleaux triangle inscribed within # in a square which in turn is inscribed # within an equilateral triangle import math as mt # Function to find the biggest # reuleaux triangle def 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 code a = 5print(Area(a)) # This code is contributed by # Mohit Kumar 29 |
chevron_right
filter_none
C#
// C# Program to find the biggest Reuleaux // triangle inscribed within in a square // which in turn is inscribed within an // equilateral triangle using System; class GFG { // Function to find the biggest // reuleaux triangle static 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 code public static void Main () { float a = 5; Console.WriteLine(String.Format("{0,0:#.00000}", Area(a))); } } // This code is contributed by Akanksha Rai |
chevron_right
filter_none
PHP
<?php // PHP Program to find the biggest Reuleaux // triangle inscribed within in a square // which in turn is inscribed within an // equilateral triangle // Function to find the biggest // reuleaux triangle function 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 code $a = 5; echo Area($a) . "\n"; // This code is contributed // by Akanksha Rai |
chevron_right
filter_none
Output:
3.79335
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
Recommended Posts:
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Biggest Reuleaux Triangle inscirbed within a square inscribed in a semicircle
- Biggest Square that can be inscribed within an Equilateral triangle
- Biggest Reuleaux Triangle within A Square
- Maximum count of Equilateral Triangles that can be formed within given Equilateral Triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Largest hexagon that can be inscribed within an equilateral triangle
- Largest right circular cylinder that can be inscribed within a cone which is in turn inscribed within a cube
- Largest right circular cone that can be inscribed within a sphere which is inscribed within a cube
- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Area of the biggest ellipse inscribed within a rectangle
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Area of circle which is inscribed in equilateral triangle
- Count of distinct rectangles inscribed in an equilateral triangle
- Area of Equilateral triangle inscribed in a Circle of radius R
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
