An equilateral triangle is drawn on the diagonal of a square.

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An equilateral triangle is drawn on the diagonal of a square. The ratio of the area of the triangle to that of the square is

Using Rule 6 and 10,
Let the side of the square be x units, then
diagonal = 2x units
∴ Area of the square = x² and area of triangle

=	√3	(√2x)²
	4

=	√ 3x²	sq. units
	2

∴ Required ratio

= x² :	√ 3x²	= 2 : √ 3 sq. units
	2