Question

The ratio of areas of incircle and circumcircle of an equilateral triangle will be ?

Answer 1

 

                                               


Let the side length of the equilateral triangle = x 

Area of incircle = (1/12) πx² 

Area of circumcircle = (1/3) πx² 

so ratio circumcircle area / incircle area = (1/3) / (1/12) ... [b/c the πx² bits cancel] 

= (1/3) * (12/1) 

= 4/1 

so area circumcircle : area incircle = 4 : 1 

Answer 2

1/4

in case of equilateral triangle, however, the ratio r/R can be found and is =1/2

so area is π *radius*radius