This work is concerned with the prediction of the elasto-acoustic properties of polydisperse solid foam structures. A highly polydisperse foam sample is first characterized using microtomography and scanning electron microscopy. Relevant geometrical properties are then determined by image processing and utilized to model the partially closed cell system with random Laguerre tessellations. The macroscopic visco-thermal transport properties of the solid foams are next calculated by numerical techniques, using either finite element computations or pore-network simulations. The permeability and sound absorption coefficient at normal incidence are also measured and a good agreement is obtained with the calculations when the elasto-acoustic coupling is modeled from the Biot's equations (including characterized visco-elastic parameters). Our results demonstrate that stochastic geometry provides a robust framework to understand the structure-property relationships of polydisperse foam.