There are 2 triangles in a circle ( triangles are in the shape of the star) What is the area of the circle not covered by traingles?

• one thing is missing length of equilateral triangle..in original questn it is 12..
  given that two equilateral triangles of length 12 has inscribed in a circle.
  
  Altitude of the triangle = (sqrt3/2)*a = √3/2(12) = 6√3
  We know that centroid divides the altitude in the ratio 2 : 1 and 2:3(Altitude) = Circum radius
  Circum radius = 2/3(6sqrt3)=4sqrt3
  Area of the circle = πr2=3.14×(4√3)^2
  Now the two triangles in the circle forms 12 small equilateral triangles with side 4. So their total area = 12×(√3/4)*a^2 = (12×√3/4)*4^2
  Area which is not covered by the equilateral triangles = 3.14×(4√3)^2 - )12×√3/4)*4^2 = 67.65 ≃68
  
• 11 years agoHelpfull: Yes(7) No(0)
• data not sufficient
• 11 years agoHelpfull: Yes(6) No(1)
• there must be a value of side or radius
  ans is (pi-1.732)R^2
• 11 years agoHelpfull: Yes(3) No(2)
• ans is 68...
• 11 years agoHelpfull: Yes(1) No(9)
• Ans: area of the circle-2*area of the each triangle
  
  where possible triangle is only isosceles triangle.
• 11 years agoHelpfull: Yes(1) No(3)
• PI*r^2-b*h
• 11 years agoHelpfull: Yes(0) No(4)
• Can you plz explain the solution Sourav.
• 11 years agoHelpfull: Yes(0) No(4)
• there is no way we can find the ans
• 11 years agoHelpfull: Yes(0) No(0)
• since two triangle form 4 isosceles triangle
  if diameter of circle is 2a
  then area of each isosceles traingle is root(2)a/4(roo(4a^2-(root(2)a)62)
  =a/2
  then area of 4 triangle is 4*a/2=2a
  area of circle is pi*a*a
  then result is pi*a^2-2a
  is it right???
• 11 years agoHelpfull: Yes(0) No(4)
• ans is = [area of circle - {2*area of triangle_1 - (2*area of triangle_2+ area of square)}]
• 11 years agoHelpfull: Yes(0) No(1)
• if the triangles are equilateral triangles then the area not covered by the triangles = area of the circle-(2*area of triangle)-area of the hexagonal part covered in the triangle twice.
  let the sides of the triangle be "a" then the sides of the hexagon will be "a/3"
  area of the hexagon=(3root3(a/3)^2)/2
• 11 years agoHelpfull: Yes(0) No(0)
• there must be a value of side or radius
  ans is (pi-1.732)R^2
  
• 10 years agoHelpfull: Yes(0) No(0)