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 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 -
**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 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.)

## Answer this Question

## Related Questions

Math problem solving - An octagonal stop sign can be cut from a square sheet of ...

Math - A cardboard manufacturer wishes to make open boxes from square pieces of ...

math - Using the Octagonal formula how do you get the 6th octagonal number 96?

college algebra - An open box is made from a square piece of cardboard 20 inches...

math - it is required to make an open box of gregreatest possible volume from a ...

calculus - A 33 by 33 square piece of cardboard is to be made into a box by ...

MATH - An open box with a square base is to be made from a square piece of ...

Analytic Geometry - A square is a quadrilateral with four equal sides. The area ...

calculus - An open box of maximum volume is to be made from a square piece of ...

math - A cardboard box manufacturer wishes to make open boxes from rectangular ...