Given side of a square a, the task is to find the side of the largest hexagon that can be inscribed within the given square.
Input: a = 6
Input: a = 8
Approach:: Let, the side of the hexagon be x and assume that the side of the square, a gets divided into smaller length b & bigger length c i.e. a = b + c
Now from the figure, we see,
b2 + b2 = x2 which gives b = x / √2
Now again, d / (2 * x) = cos(30) = √3 / 2 i.e. d = x√3
And, c2 + c2 = d2 which gives c = d / √2 = x√3 / √2
Since, a = b + c. So, a = x / √2 + x√3 / √2 = ((1 + √3) / √2) * x = 1.932 * x
So, side of the hexagon, x = 0.5176 * a
Below is the implementation of the above approach:
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