The ratio of the area of an equilateral triangle and that

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The ratio of the area of an equilateral triangle and that of its circumcircle is

Let AB = BC = AC = 2x units
AD = √4x² - x² = √3x

OD =	1	× √3x =	x
	3		√3

∴ OB = √x² +	x²
	3

=	2x²	= Circum radius
	√3

=	√3	× 4x² : π ×	4x²
	4		3

= 3√3 : 4π