Information on landscape structure is an important issue for sustainable development and for making correct spatial planning decisions. Therefore, studies providing information on the diversity and changes of land cover and land use in a selected area are currently an important research topic. In addition to quantitative-qualitative statistics, spatial entropy is increasingly used to assess the degree of diversity of land cover and land use. This paper aim was to determine the diversity of objects within the land cover classes in the years 2014, 2017 and 2020, with a focus on built-up areas, in three districts bordering the city of Kraków, i.e. the Wieliczka, Kraków and Proszowice districts, located in the Małopolskie Voivodeship in Poland. In order to perform the analysis with the appropriate spatial resolution, a hex grid was used to determine the diversity of objects in the built-up area class. For this reason, data on land cover from the BDOT10k national database of topographic objects were used. The analyses followed the division into classes and objects defined in the structure of the BDOT10k database. The degree of diversity was determined using the Entropy Index and Herfindahl-Hirschman Index. Changes in the diversity of built-up areas were observed especially in areas located in close proximity to the border of Kraków, as well as on its eastern and south-eastern sides. A significant relationship was also observed between the increase in diversity of objects in the built-up area class and the immediate proximity of roads.