An equilateral triangle and a regular hexagon have equal parameters then what is the ration of their areas?
A) 6:1
b) 1:6
c) 3:2
d) 2:3

• Regular hexagon=6 equilateral triangles
  => area of equilateral triangle =root(3)/4*a^2
  => area of hexagon= 6 *(root(3)/4*a^2)=3*(root(3)/2*a^2)
  So, ratio of their areas is 1:6
• 11 years agoHelpfull: Yes(16) No(10)
• area of triangle=root(3)a^2/4
  area of hexagon=root(3)*3b^2/2
  perimeter are same so hexagon b =a/2
  (root(3)a^2/4)/(root(3)*3(a/2)^2/2)
  so,result will be 2:3
• 11 years agoHelpfull: Yes(9) No(0)
• area of equilateral=root(3)/4*a^2
  area of hexagon=6*a^2*root(3)/4
  solving two equations
  ans=1:6
• 11 years agoHelpfull: Yes(1) No(7)
• area of equilateral triangle=(sqrt3/4)s^2
  area of hexagon=(3sqrt3/2)s^2
  ans= 1:6
• 11 years agoHelpfull: Yes(0) No(5)
• FOR A HEXAGON
  Perimeter = 6 * radius
  Area = (3√3/2) * (radius)^2
  FOR AN EQUILATERAL TRIANGLE
  Perimeter = 3 * side
  Area = (side^2)√3/4
  Since Hexagon perimeter = Equilateral triangle perimeter
  then 6 * radius = 3 * side
  Divide both sides of the equal sign by 3.
  6 * radius / 3 = 3 * side / 3
  6 * radius / 3 = side
  Flip the equation around.
  side = 6 * radius / 3
  side = 2 * radius
  This equation above gives me the relationship I needed between the radius and the side variables.
  
  Next we deal with the ratio of the areas by using their area formulas.
  
  . . . Area of hexagon . . . . . . (3√3/2)(radius)^2
  -------------------------------------- = --------------------------
  Area of equilateral triangle . . . (side^2)√3/4
  
  Expand the exponent variables
  
  . . . Area of hexagon . . . . . . (3√3/2)(radius)(radius)
  -------------------------------------- = --------------------------------
  Area of equilateral triangle . . (side)(side)√3/4
  
  Since we calculated that side = 2 * radius, then substitute 2radius for side.
  
  . . . Area of hexagon . . . . . . (3√3/2)(radius)(radius)
  -------------------------------------- = --------------------------------
  Area of equilateral triangle . . (2radius)(2radius)√3/4
  
  cancel out common terms radius and radius
  
  . . . Area of hexagon . . . . . . (3√3/2)
  -------------------------------------- = ---------------
  Area of equilateral triangle . . (2)(2)√3/4
  
  . . . Area of hexagon . . . . . . (3√3)/2
  -------------------------------------- = ------------
  Area of equilateral triangle . . 4(√3)/4
  
  cancel out common terms 4 and √3
  
  . . . Area of hexagon . . . . . . 3/2
  -------------------------------------- = -----
  Area of equilateral triangle. . . 1
  
  . . . Area of hexagon. . . . . . . 3
  -------------------------------------- = -----
  Area of equilateral triangle. . . 2
  
  
• 9 years agoHelpfull: Yes(0) No(3)