March 29, 2017

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There is a square with each of it’s side is of 2m. An octagonal is cut-of 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 - ,

    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√2)/(2+√2)
    = 0.8284 m (approx.)

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