What is the largest Rayleigh triangle inside a square?

Here we will see the area of ​​the largest Reuleaux triangle inscribed in a square. The side of the square is "a". The height of the Reuleaux triangle is h.

The height of the Reuleaux triangle is the same as a. So a=h. So the area of ​​Reuleaux triangle is -

Example

#include <iostream>
#include <cmath>
using namespace std;
float areaReuleaux(float a) { //side of square is a
   if (a < 0) //if a is negative it is invalid
      return -1;
   float area = ((3.1415 - sqrt(3)) * (a) * (a))/2;
   return area;
}
int main() {
   float side = 8;
   cout << "Area of Reuleaux Triangle: " << areaReuleaux(side);
}

Output

Area of Reuleaux Triangle: 45.1024

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