Since the triangle is equilateral, the center of the circle is not only the incenter but the centroid. Therefore, the height of the triangle is in a 3:1 ratio with the radius of the circle. Assuming a unit circle, the height is 3, and the area is 3*sqrt(3). The square's area is 1.

Triangle:Square = 3sqrt(3)/4.

[Edit]: Haha fuck, the squares area is 4, lulz.