For a circle of radius $ r $ and an arc of $ \theta $ degrees, the arc length is $ (2\pi r)\frac{\theta}{360} $. Thus, for the same arc length, the arc angle is inversely proportional to the radius, so the ratio of the radius of circle $ A $ to the radius of circle $ B $ is $ 40:55 $, or $ 8:11 $. Since the ratio of the areas of two circles is the square of the ratio of their radii, the ratio of the area of circle $ A $ to the area of circle $ B $ is $ (8/11)^2=\boxed{\frac{64}{121}} $.