an equilateral triangle of side 18cm is cut and a regular hexagon of the lagrest possible side is carved out of it. find the area of hexagon.

• 54 sqrt (3) as equliateral triangle side =18cm divide this side into 3 equal parts =18/3=6 ;; area of hexagon = 3*sqrt(3) /2 (side)^2 =3*sqrt(3)/2 (6)^2 = 54 sqrt(3)
• 9 years agoHelpfull: Yes(14) No(7)
• An equilateral triangle of side 18cm is cut and a regular hexagon of the lagrest possible side is carved out of it. find the area of hexagon
  A. 120.5√3
  B. 123.5√3
  C. 121.5√3
  D. 124.5√3
  
  solution
  Perimeter of hexagon=Perimeter of triangle
  6a=3a
  6a=3*18
  a=9
  area of hexagon = 6*(√3/4)a^2
  =121.5√3
• 9 years agoHelpfull: Yes(13) No(1)
• Perimeter of Hexagon= 6a
  6a=18x3
  a=9
  
  Area of Hexagon= (3)((3)^1/2)(a^a)/2 = (3^5)(3^1/2)/2
  
• 9 years agoHelpfull: Yes(12) No(15)
• Dear Pradeep,
  18 cm is length of one side According to your solution there will be nine sides in hexagon.please elaborate further
  Now,
  Perimeter of triangle=54
  thus one side's length=54/6=9cm
  thus area=243sqrt(3)/2
  
• 9 years agoHelpfull: Yes(6) No(2)
• 93.53 or= 54 Sqrt 3.
  
  Divide the side into three equal parts and fold the triangle at the three corners.
  
  Area = (3 Sqrt 3 * 6)/2 = 54 Sqrt 3
• 9 years agoHelpfull: Yes(3) No(3)
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  The required figure takes this shape
  
  For a regular hexagon of the largest possible side to fit inside an equilateral triangle length of each side of the hexagon must be equal to 1/3rd length of the
  side of the equilateral triangle.
  
  So, length of each side of the hexagon is 18/3 = 6cm.
  
  Area of the hexagon = 0.433*side*side = 0.433*6*6 = 15.59
• 9 years agoHelpfull: Yes(2) No(2)
• I created the figure 4 this question, but after posting my answer all the sequence of the diagram got disturbed, so the diagram did not come clearly....
• 9 years agoHelpfull: Yes(2) No(0)
• formula for hexagon from equilateral triangle is 6*(sqrt(3)/4)*side_square
• 9 years agoHelpfull: Yes(1) No(0)
• here given side of equilateral triangle=18cm
  let side of hexagon=acm
  perimeter of hexagon=perimeter of euilateral traingle
  6a=3*side of traingle
  6a=3*18
  a=9cm
  area of hexagon =3*sqrt(3)/2 *(side)^2
  =3*sqrt(3)/2 *(9)^2
  =121.5sqrt(3)
  ans c
  
• 8 years agoHelpfull: Yes(1) No(0)
• plzzz..pradeep explain in detail..
• 9 years agoHelpfull: Yes(0) No(1)
• the largest possible polygon from the triangle will be drawn inside the incircle
  of the given triangle.
  now the area of incircle of an equilateral triangle of side X is (pi/12)*x^2
  => radius of incircle =sqrt(27)=3*sqrt(3)
  now if we will draw the hexagon within this circle then each side will be equal to 3*sqrt(3) now if we join the all the vertices of the hexagon through diagonals of hexagon then we will get 6 equilateral triangle of side 3*sqrt(3)
  =>area of 1 triangle = (sqrt(3)/4)*(3*sqrt(3))^2=(27*sqrt(3))/4
  area of 6 triangle = area of hexagon=6*(27*sqrt(3))/4=(81*sqrt(3))/2=70.148
• 9 years agoHelpfull: Yes(0) No(2)
• u can use direct formula.here..formula to find out area of regular polygons is.. n*s^2/4*cot(180/n)..where....n=no of side.and s= length of side....
  in this question n=6 and side length is 54/6=9. so area==6*9*9/4 * cot(180/6) it results in......81*6(root 3)/4...!
• 9 years agoHelpfull: Yes(0) No(0)
• AREA OF A EQUILATERAL TRIANGLE= SQRT(3)*(SIDE)^2/4.
  AREA=SQRT(3)*(18)^2/4
  AREA OF LARGEST REGULAR HEXAGON =6* SQRT(3)*(18)^2/4. [as a regular hexagon comprises of 6 equilateral triangles]
  AREA=486*SQRT(3).
• 9 years agoHelpfull: Yes(0) No(0)
• perimeter of hexagon= 18*3= 54
  side of hexagon= 54/6= 9
  area of hexagon= [{3* sqrt(3)} /2] * 9^2 ]
• 9 years agoHelpfull: Yes(0) No(0)
• Ans:c)121.5/cub root(3)
  Sol:
  Formula for Area of Equilateral triangle =cub root(3)*a*a/4 where a is length of Equilateral triangle
  Area of triangle is =cub root(3)*18*18/4=4.5*3/cub root(3) cm^2
  Area of hexagon=6*cub root(3)*b*b/4 where b is side of hexagon
  largest area is carved out of it =Area of triangle - Area of Hexagon
  =4.5/cub root(3-b*b) cm^2
  check the of option should be divisible by 4.5/cub root(3)
  we get option c
• 8 years agoHelpfull: Yes(0) No(0)