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:
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Biggest Reuleaux Triangle within A Square
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Biggest Reuleaux Triangle inscirbed within a square inscribed in a semicircle
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Area of a triangle inside a parallelogram
- Area of Incircle of a Right Angled Triangle
- Area of Circumcircle of a Right Angled Triangle
- Program to find area of a triangle
- Check if right triangle possible from given area and hypotenuse
- Area of a largest square fit in a right angle triangle
- Maximum area of triangle having different vertex colors
- Minimum height of a triangle with given base and area
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