This thesis shows highly encouraging results as the gain of accuracy reached 18.4% when the pairwise comparisons method was used instead of the direct method for comparing random shapes. The thesis describes a heuristic for generating random but nice shapes, called placated shapes. Random, but visually nice shapes, are often needed for cognitive experiments and processes. These shapes are produced by applying the Gaussian blur to randomly generated polygons. Afterwards, the threshold is set to transform pixels to black and white from di erent shades of gray. This transformation produces placated shapes for easier estimation of areas. Randomly generated placated shapes are used to perform the Monte Carlo method to test the accuracy of cognitive processes by using pairwise comparisons. An on-line questionnaire has been implemented and participants were asked to estimate the areas of ve shapes using a provided unit of measure. They were also asked to compare the shapes in pairs. Such Monte Carlo experiment has never been conducted for 2D case. The received results are of considerable importance.