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:
# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is
# inscribed within a hexagon
# Function to find the biggest
# reuleaux triangle
# side cannot be negative
if (a < 0): return -1 # height of the reuleaux triangle h = 1.268 * a # area of the reuleaux triangle A = 0.70477 * math.pow(h, 2) return A # Driver code a = 5 print(Area(a),end = "\n") # This code is contributed # by Akanksha Rai [tabby title="C#"]
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- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of the Largest Triangle inscribed in a Hexagon
- Largest hexagon that can be inscribed within an equilateral triangle
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- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
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