Given a regular hexagon of side length a which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Input: a = 5 Output: 28.3287 Input: a = 9 Output: 91.7848
Approach: As the side of the square inscribed within a hexagon is x = 1.268a. Please refer Largest Square that can be inscribed within a hexagon.
Also, in the reuleaux triangle, h = x = 1.268a.
So, Area of the reuleaux triangle, A = 0.70477*h^2 = 0.70477*(1.268a)^2.
Below is the implementation of the above approach:
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