Posted by soumya on Sunday, January 9, 2011 at 4:22am.
There is a square with each of it’s side is of 2m. An octagonal is cutof from this square by cutting it’s edge such that the octagonal has all it’s sides equal. Find out the length of each side of the octagonal

math  MathMate, Sunday, January 9, 2011 at 8:14am
We would need to cut out four corners to make a regular octagon (all 8 sides of equal length) from the square.
Each corner cut out will be an isosceles rightangled triangle with short sides of length x, and hypotenuse (√2)x.
Since the hypotenuse forms one side of the octagon, all eight sides are of length (√2)x.
The length of one side of the square is therefore:
L = x + (√2)x + x = 2 m
Solving for x:
(1 + √2 + 1)x = 2
x = 2/(2+√2)
and the length of each side of the octagon is
(√2)x
= (2√2)/(2+√2)
= 0.8284 m (approx.)
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