The perimeter of an equilateral triangle is equal to a regular hexagon. Find out the ratio of their areas?

• area of equilateral triangle : area of hexagon
  root(3)/4 a^2 : 3root(3)/2 b^2 -> 1
  then perimeter of triangle =3a
  perimeter of hexagon = 6a
  therefore by equating a=2b sub in 1
  then the ratio is 2:3.
• 5 years agoHelpfull: Yes(3) No(2)
• 3a=6b
  a:b=2:1
  (sqrt(3)/4)a^2:(3sqrt(3)/2)b^2
  ans 2:3
• 5 years agoHelpfull: Yes(1) No(0)
• as perimeter of triangle is equal 3a=6a i.e 1:2,...so areas are also equal (root(3)/4)*a^2=(3root(3)/2)*a^2
  so ratio is 3:2 so therefore,answer is 3:2
• 5 years agoHelpfull: Yes(0) No(1)
• Find height of triangle i.e (root(3) *R / 2)
  As, perimeter of triangle = perimeter of hexagon
  3R = 6A -> R = 2A -> A = R/2
  area of triangle = area of hexagon
  (1/2 * R * root(3) * 1/2) = (3 * root(3) * (R/2)^2 /2)
  that gives ratio 2:3
• 5 years agoHelpfull: Yes(0) No(1)
• side of equilateral triangle = a
  hexagon = s
  3a = 6s
  ratio of area
  
  3*root 3 a**2 /4 : 3*root 3 (1/2a)**2 / 2
  Ans = 2:3
• 3 years agoHelpfull: Yes(0) No(0)