What is the area of ​​the Luer triangle?

Here we will see how to calculate the area of ​​the Reuleaux triangle below. There is an equilateral triangle inside a Reuleaux triangle. Assuming its height is h, this shape is composed of the intersection of three circles.

There are three circular sectors. The area of ​​each sector is −

#Since the area of ​​an equilateral triangle is added three times, we must subtract them. Therefore the final area is −

Example

#include <iostream>
#include <cmath>
using namespace std;
float areaReuleaux(float h) {
   if (h < 0) //if h is negative it is invalid
   return -1;
   float area = ((3.1415 - sqrt(3)) * h * h)/2;
   return area;
}
int main() {
   float height = 6;
   cout << "Area of Reuleaux Triangle: " << areaReuleaux(height);
}

Output

Area of Reuleaux Triangle: 25.3701

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