Incircle area and circumcircle area of an Equlateral triangle
Perimeter of equilateral triangle = 3 × side
Height (altitude) of an equilateral triangle = side × (√3) /2
Area of an equilateral triangle = side² × (√3) /4.
In equilateral triangle orthocentre, centroid, incentre and circumcentre coinside at the same point.
In the figure R= circum radius ; r= In radius
Centroid (circumcentre, Incentre ) divides median in 2:1 ratio.( median length divided in 2:1 ratio 2 parts equal to circum radius 1 part equal to in radius)
In equilateral triangle median and altitude coincide with each other. So centrod divides altitude in 2:1 ratio
Inradius of an equilateral triangle =
¹/₁₊₂ × height = ⅓ × height = side × (√3) /6. {∵ height = side × (√3) /2}
Circumradius of an equilateral triangle =
²/₁₊₂ ×height = ⅔ × height = side / √3
Incircle area of an equilateral triangle = 𝝅 r² = 𝝅 { side × (√3) /6}². =side² × π / 12
Circumcircle area of an equilateral triangle = 𝝅 R² = 𝝅 {side / √3}² = side² × π / 3
Circumradius = 2 × Inradis
