Given a regular Hexagon with side length a, the task is to find the area of the circle inscribed in it, given that, the circle is tangent to each of the six sides.
Input: a = 4 Output: 37.68 Input: a = 10 Output: 235.5
From the figure, it is clear that, we can divide the regular hexagon into 6 identical equilateral triangles.
We take one triangle OAB, with O as the centre of the hexagon or circle, & AB as one side of the hexagon.
Let M be mid-point of AB, OM would be the perpendicular bisector of AB, angle AOM = 30 deg
Then in right angled triangle OAM,
tanx = tan30 = 1/√3
So, a/2r = 1/√3
Therefore, r = a√3/2
Area of circle, A =Πr²=Π3a^2/4
Below is the implementation of the approach:
- Area of a square inscribed in a circle which is inscribed in a hexagon
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of the Largest Triangle inscribed in a Hexagon
- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of circle inscribed within rhombus
- Area of decagon inscribed within the circle
- Area of circle which is inscribed in equilateral triangle
- Program to find Area of Triangle inscribed in N-sided Regular Polygon
- Find the area of largest circle inscribed in ellipse
- Program to calculate area of an Circle inscribed in a Square
- Area of largest Circle inscribe in N-sided Regular polygon
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Find area of the larger circle when radius of the smaller circle and difference in the area is given
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.