Maybe, it's a useless question. The figure which I'm talking about consists of two parallel lines each of length 'b' and are separated by a distance 2r. Their ends on one side is closed by a semicircle which in pointing inwards and decreases the area and the ends on the other side are joined by another semicircle of the same radius 'r' but this time it is bulging outwards and contributes to the area. So, we have a closed figure. Finding its area is simple because the amount of area decreased by the first semicircle gets added again by the second semi-circle. So, the area remains the same as that of a rectangle with length 2r and breadth b. A=2rb. But I get a different answer by this reasoning: The given figure can be thought to be made up of an infinite number of semicircular arcs from top to bottom. The figure is filled with semicircles. So, the area of this figure can be thought to be the sum of the lengths of these infinite number of semicircles. The length of each elementary semicircle, i.e. pi*r is constant. And, these semicircles are distributed over a length 'b'. So, the area of the figure = pi*r*b, which is wrong. But, what is wrong with this reasoning?