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:
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- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of the circle that has a square and a circle inscribed in it
- 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
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- 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
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