Two equilateral triangle of side 12cm are placed one on top another, such a 6 pointed star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the Star?
a)61
b)57
c)68
d)83
My answer: 68

• two triangle will form 12 euqilateral triangle of side 4 cm
  so area covered=12*((root 3/4)*4*4)=80.2
  from bigger triangle we can calculate altitude i.e=6root3
  from smaller triangle we can calculate altitude i.e=2root3
  so diameter becomes 8root3 and hence radius=4root3
  area of circle=pi*(4root3)sqr=150.2
  unshaded area=150.2-82.08=68(approx)
• 11 years agoHelpfull: Yes(19) No(8)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(7) No(0)
• @shailesh..how twelve triangles?
• 11 years agoHelpfull: Yes(6) No(3)
• the ans is approx 68
• 11 years agoHelpfull: Yes(2) No(2)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(1) No(0)
• 
  two triangle will form 12 euqilateral triangle of side 4 cm
  
  
  area covered=12*((root 3/4)*4*4)=80.2
  from bigger triangle we can calculate altitude i.e=6root3
  from smaller triangle we can calculate altitude i.e=2root3
  so diameter becomes 8root3 and hence radius=4root3
  area of circle=pi*(4root3)sqr=150.2
  unshaded area=150.2-82.08=67.71)
  
• 10 years agoHelpfull: Yes(1) No(0)
• explain the shailesh kumar method briefly
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(0)
• ans to your ques kartika is:
  6 triangles touching the circumference of the circle and remaining 6 touch the centre and the base of the triangle touching the centre and circumference is the same.hence 12 triangles.
  now how the side of the triangle is calculated:
  side of the bigger two triangles is 12 so their altitude is (root3/2)12 i.e.6root3
  now centroid divides the altitude in the ratio 2:1.hence circumradius is (2/3)of altitude which becomes 4root3.from this area of the circle can be calculated.
  Now one third of altitude of the bigger triangle forms the altitude of the smaller triangle.
  hence by the formula (root3/2)*side=altitude we can find side of the smaller triangle.
  
• 10 years agoHelpfull: Yes(0) No(3)