A geometrically asymmetric trapezoidal fin with fluid in the inside wall is optimized based on the fixed fin volume using a one-dimensional analytic method. The variation of temperature along the normalized X position in the fin is presented. For the fixed fin volumes, the maximum heat loss, the corresponding optimum fin effectiveness, fin base height and fin length (or fin tip length) as a function of the fin base thickness, fin shape factor and the fin volume are represented. One of the results shows that both the optimum fin length and the optimum fin base height decrease with the increase of the value of fin shape factor.