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

Here we will see the area of biggest Reuleax triangle inscribed within a square which is inscribed in an equilateral triangle. Suppose ‘a’ is the side of the triangle. The side of the square is x and the height of the Reuleaux triangle is h.

The side of the triangle is −

So the value of x is −

𝑥 = 0.464𝑎

The height of the Reuleaux triangle is the same as x. So x = h. So the area of the Reuleaux triangle is −

## Example

#include <iostream> #include <cmath> using namespace std; float areaReuleaux(float a) { //side of triangle is a if (a < 0) //if a is negative it is invalid return -1; float area = ((3.1415 - sqrt(3)) * (0.464*a) * (0.464*a))/2; return area; } int main() { float side = 5; cout << "Area of Reuleaux Triangle: " << areaReuleaux(side); }

## Output

Area of Reuleaux Triangle: 3.79311

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