Let the length of an equilateral triangle be a, draw the largest circle in the equilateral triangle as its inscribed circle, and the radius r=a/3.

The largest equilateral triangle in this circle is the triangle inscribed in the circle, and the relationship between its side length and the radius of the circle is side length = 2/3 * R.

So the side length of a small triangle is (a/3)÷(2/3)=a/2.

The side length of a small triangle is 1/2 that of a large triangle.

Small triangle area: large triangle area = 1: 4.