The heat that transferred through conduction in a body, should be discharged through convection process frequently. In continuous years, heat and fluid science has tried to find characteristics of the transfer in variety configurations. This information is vital for designing and analyzing of the system. But the problem is that there are many constraints and one of the most important of them, is space (measure-volume-weight). The goal is always to transfer much more heat in a specific space. But the active temperature might be more than the desired temperature. Whereas the function of this equipment has a direct relevance with temperature, it is very important to keep the equipment at an acceptable temperature. Sometimes it is required to cool a hot plate or keep it in a constant temperature without using forced convection heat transfer. In this case, it sounds a good way to use fin in free convection heat transfer. In the present study, the goal is to optimize free convection heat transfer from a finned hot plate. Many different algorithms and methods are used in optimizations. One of these methods is constructional theory. Unlike thermodynamic optimization, in which we try to have a unique balance (for minimum irreversibility) between heat transfer function and fluid mechanics function, in constructal theory the goal is to find a pattern, in which both of these functions reach the highest possible level. By using constructal theory, we can get fins geometry such as height and thickness, number of the fins and their positions, to transfer maximum heat from them with considering specific constraints. These constraints are temperature of the hot plate, mass of the material which we decide to make fins from, degrees of freedom including thickness of the fins, height of the fins, degree of the hot plate with azimuth and distance of the fins from each other. For theoretical solution, free convection heat transfer relation and intersection of asymptotes method are used. In addition to theoretical solution, the problem also was solved numerically and both results was analyzed and compared to each other. Finally the optimized structure was gotten. In one case, thickness of the fins was considered constant and their height and distance between them were optimized. In the other case, smaller fins were located among the other fins to use the unheated space among them. In these two cases, the results of solution with intersection of asymptotes method and numerical solution with computer aid were coincided. in continuance, the effect of dimension on increasing heat transfer from fins and optimized geometry was investigated. In surveying the angel of the base plate with azimuth, two different cases were considered. In one case the base plate had fin and in the other case it did not have any fins. In addition, the difference of heat flow rate between the plate and fins was studied in two cases. Keywords: finned plate, free convection heat transfer, geometric optimization, constructal theory, intersection of asymptotes.