Area of Reuleaux Triangle
Given an integer h which is the side of an equilateral triangle formed by the same vertices as the Reuleaux triangle, the task is to find and print the area of the Reuleaux triangle.
Input: h = 6
Input: h = 9
Approach: The shape made by the intersection of the three circles ABC is the Reuleaux Triangle and the triangle formed by the same vertices i.e. ABC is an equilateral triangle with side h.
Now, Area of sector ACB, A1 = (π * h2) / 6
Similarly, Area of sector CBA, A2 = (π * h2) / 6
And, Area of sector BAC, A3 = (π * h2) / 6
So, A1 + A2 + A3 = (π * h2) / 2
Since, the area of the triangle is added thrice in the sum.
So, Area of the Reuleaux Triangle, A = (π * h2) / 2 – 2 * (Area of equilateral triangle) = (π – √3) * h2 / 2 = 0.70477 * h2
Below is the implementation of the above approach:
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