Dissipative mufflers are often used for the reduction of broadband noise transmitted in ducts. Many common calculation procedures for the transmission loss of such mufflers require conventional shapes like rectangular or circular cross-sectional areas. In an effort to analyze the effect of the cross-sectional area of dissipative mufflers on the resulting noise reduction, the transmission loss of axially uniform mufflers with polygonal cross-sectional areas was investigated using the finite element method. The mufflers are designed to have the same open area, and hence in a practical application would lead to a similar pressure drop. The results were compared to those obtained with the well known approximative method of Piening. Good agreement between simulation and estimation was found regarding basic trends at low frequencies, while notable differences were revealed regarding the maximum transmission loss.