The hardness of the bulky or covered materials is typically obtained through indentation techniques. Due to the complexity of the influence of the micro- or nanohardness of the coating and the substrate on the measuring of the composite hardness, various mathematical and geometrical models based on the area law-of-mixtures’ advance are founded. The present study offers mathematical and geometrical modelling of the coefficient of the area law-of-mixtures' for conical indentation. The project imprints are considered as disks and the coefficients $\alpha$, $\beta$ of the area law of mixtures become ratios of circle surfaces. The hardness of the composite and the substrate is expressed as a function of the imprint projected dimensions and the applied load. Finally, the film contribution is determined from the proposed modelling of the area law-of-mixtures’ model.