Posted by soumya on Sunday, January 9, 2011 at 4:22am.
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 right-angled 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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