In some previous papers the authors consider some Laplace type for different lattice, in particular in (7) the authors consider a Laplace type for a trapezoidal lattice with rectangle body test. In this paper we consider a lattice with fundamental cell composed by a trapetium but for the first time we consider as body test a random rectangle not uniformly distributed. We compute the probability that a random rectangles of constant sides intersects the a side of lattice when the position of rectangle is a random variable with exponential and distibution. I. INTRODUCTION In 1773, at a meeting of the Academic des Sciences de Paris, Buffon posed a that later on should become knows as the famous Buffon needle problem : in a room, the floor of which is merely divided by parallel lines, at a distance a apart, a needle of length is allowed to fall at random: which is the probability that the needle intersects one of the lines? The solution, determined by Buffon by means of empirical methods, was . The and its solution were published in 1777, in the Comptes rends de l'Academie des sciences de Paris . In 1812, Laplace extended the by considering a room paved with equal tiles, shaped as rectangles of sides and , with The solution was , and it is obvious that the probability of Buffon can be obtained from that of Laplace by letting .