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

From the formula of each side of inscribed square inside one hexagon is −

𝑥 = 1.268𝑎

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

#include <iostream> #include <cmath> using namespace std; float areaReuleaux(float a) { //side of hexagon is a if (a < 0) //if a is negative it is invalid return -1; float area = ((3.1415 - sqrt(3)) * (1.268*a) * (1.268*a))/2; return area; } int main() { float side = 5; cout << "Area of Reuleaux Triangle: " << areaReuleaux(side); }

Area of Reuleaux Triangle: 28.3268

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