Two equilateral triangles of side 12cm are placed one on top of another, such that a 6 pointed star is formed. If the 6 vertices lie on a circle, what is the area of the circle not enclosed by the star? (Give answer to the nearest square cm)

• dear m4 maths everyone solves the quetions and gives diffrent answers . Please check and display the correct answers only. Dont display the wrong answers. We are totally confused about the solutions given by differnt people.
• 11 years agoHelpfull: Yes(45) No(0)
• answer is 68cm^2 approx
• 11 years agoHelpfull: Yes(16) No(4)
• radius of circumcircle of equilateral triangle=a/root 3
  area of equilateral triangle is=root 3/4 *(a)
  so,area remaining=area of circle-(area of triangle of side 12 +3*area of triangle with side 4)
  =3.14*(12/root 3)^2-(root 3/4*(12)^2+3*root 3/4*(4)^2)
  =83.174
• 11 years agoHelpfull: Yes(7) No(7)
• 
  Altitude of the triangle = 3√2a = 3√2(12) = 63√
  We know that centroid divides the altitude in the ratio 2 : 1 and 23(Altitude) = Circum radius
  Circum radius = 23(63√)=43√
  Area of the circle = πr2=3.14×(43√)2
  Now the two triangles in the circle forms 12 small equilateral triangles with side 4. So their total area = 12×3√4a2 = 12×3√442
  Area which is not covered by the equilateral triangles = 3.14×(43√)2 - 12×3√442 = 67.65 ≃68
• 10 years agoHelpfull: Yes(7) No(0)
• Area = area of circle -(area of whole triangle of side 12cm + 3*area of triangle of side 4cm )
  radius of circle is 4 under root 3, area of equilateral triangle root3/4 side square
  Ans =3.88cm^2
• 11 years agoHelpfull: Yes(2) No(4)
• how did you get it??????
  
• 11 years agoHelpfull: Yes(2) No(0)
• soory i have made mistake in calculations,approach is correct but correct ans is 68 only
• 11 years agoHelpfull: Yes(2) No(1)
• plzz explain soumyadeep saha
• 11 years agoHelpfull: Yes(1) No(0)
• 81cm square
• 11 years agoHelpfull: Yes(0) No(3)
• explain soumyadeep(bacchan)
• 11 years agoHelpfull: Yes(0) No(0)
• the correct solution should be given by M4 maths only as different people have diff ans
• 9 years agoHelpfull: Yes(0) No(0)