Given a square of length 2m. Its corners are cut such that to represent a regular octagon. Find the length of side of octagon.

• let us assume that every corner in every side cut by x m.
  so, the length of side of octagon =2-(x+x)=2-2x=2(1-x)m.
  from pythagoras' theorem, sqrt(x^2+x^2)=2-2x
  or, x*sqrt(2)=2-2x
  or, x(2+sqrt(2))=2
  or, x=2/(2+sqrt(2))=2-sqrt(2)
  thus, side of polygon=2(1-2+sqrt(2))=2*(0.4142)=0.8284m
• 11 years agoHelpfull: Yes(14) No(3)
• Let a=length of side of polygon, r be inradius of octagon,n=8(number of sides of octagon)
  then formula
  a=2r*tan(pi/n) (pi=180degrees)
  therefore lenght of side a=0.8284
• 11 years agoHelpfull: Yes(6) No(1)
• Let x is the side of the octagon and x + 2y is the side of the square.
  In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2√
  But x2√+x+x2√=2
  ⇒2√x+x=2
  ⇒x=22√ +1=22√ +1×2√ −12√ −1=2(2√ −1)
• 11 years agoHelpfull: Yes(1) No(1)
• since it is given as square inradius r= (side of square)/2
• 11 years agoHelpfull: Yes(0) No(1)
• use formula for side for side inscribed octagon.
  we will have a/sqrt(2)+a+a/sqrt(2)=2
  ans will be 0.823
• 11 years agoHelpfull: Yes(0) No(1)
• Let x is the side of the octagon and x + 2y is the side of the square.
  In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2√
  But x2√+x+x2√=2
  ⇒2√x+x=2
  ⇒x=22√ +1=22√ +1×2√ −12√ −1=2(2√ −1)
• 11 years agoHelpfull: Yes(0) No(0)