Question 901096: A customer of Karmis Carpet in Glen Ellyn needed an area rug for their foyer I the shape of a regular octagon. The rug was to be cut from a 12 for square piece of carpet. Mr. Chris Karmis needed to know the side length of the regular octagon. Your task is to determine the side length of the regular octagon. Also, generalize the solution if the rug is to be cut from a k foot square piece of carpet.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Mr. Chris Karmis would be cutting an isosceles right triangle out of each corner of the square.
If the legs of each right triangle measure  feet,
the hypotenuse length, in feet, is
 ,
and that is the length of each of the sides of the regular octagon.
  -->  -->  ,
and  , or  is the length, in feet, of the side of the octagon.
Since math teachers do not like to see square roots in denominators, we could rationalize those expressions.
 ,
and  .
Of course, Mr. Chris Karmis would like to know an approximate measure, in feet, so we would tell him that the side of the octagon measures  feet.
If Mr Karmis had a square piece of carpets with sides measuring  feet,
the equation would be
 --> 
and the length of the side of the octagon would be
 .
For Mr. Karmis sake, we would give an approximate answer:
the length of the side of the octagon, in feet, can be calculated as
 .
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