From a square of side 2 cm, equal triangles are cut from its corners to form a regular octagon. We will get an octagon. What is the area of that octagon?

• Let x = side of the regular octagon. By symmetry, each figure cut from the corners must be an isosceles right (45-45-90) triangle,
  and all four of them must be congruent. Then the leg of each isosceles triangle must have measure x/sqrt(2)
  Then we must have x/sqrt(2)+x+x/sqrt(2)=2, or
  after simplification,
  x= 2/(1+sqrt(2)) this is one side of octagon .
  Area of octagon =2(1+sqrt(2))a^2, where a is side of octagon,
  area of octagon =2(1+1.414)(2/(1+sqrt(2)))^2
  =3.31 cm^2
  
• 8 years agoHelpfull: Yes(8) No(1)
• 8(sqrt2)-8
• 8 years agoHelpfull: Yes(3) No(3)
• Area = area of square - 4 * 1/2*0.5*0.5 = 4 - 0.5 = 3.5
• 8 years agoHelpfull: Yes(2) No(1)
• plz provide detailed explainaition!!
• 8 years agoHelpfull: Yes(2) No(0)
• 4-4(1/2*2/3*2/3)=3.12
• 8 years agoHelpfull: Yes(2) No(0)
• area of regular octagon formed=3.304 cm^2.
• 8 years agoHelpfull: Yes(1) No(5)
• 77.25 or 32(1+sqrt(2))
  
• 8 years agoHelpfull: Yes(0) No(0)