In this study, a polygonal approach is suggested to generalize the notion of the confidence region of the univariate probability density function for the bivariate probability density function. The equal density approach is used to demonstrate that confidence regions can be polygonal shapes. The bisection method is the preferred method in finding the equal density value that reveals the desired confidence coefficient. Confidence regions estimate not only bivariate unimodal probability functions but also bivariate multimodal probability functions. An approach is enhanced to estimate these confidence regions for probability density functions which are defined as rectangular, polygonal and infinite expanse areas. In order to show the applicable of the proposed method, four different examples are analyzed. The results show that the confidence region is found no matter how complex the distribution function. In addition, the proposed method gives more efficient results for multimodal probability density functions.