Optimum fin effectiveness of geometrically and thermally asymmetric trapezoidal fins is represented as a function of the ratio of the fin bottom to top Biot numbers, the ratio of the fin tip to top Biot numbers and fin shape factor. Optimum fin effectiveness is taken as 98% of the maximum fin effectiveness by comparing the increasing rate of fin effectiveness with that of dimensionless fin length. For this analysis, two dimensional separation of variables method is used. Also, the value of the slope of upper surface of the fin and fin efficiency corresponding to optimum effectiveness are presented.