# Linear and Nonlinear Modelling of the Usable Area of Buildings with Multi-Pitched Roofs
Such documents and permit applications are required to start using the buildings. Using data from BDOT10k to estimate usable area has the potential to solve several problems of Polish appraisers. We propose the use of mathematical modelling to estimate the usable area of residential buildings with multi-pitched roofs based on topographic data. Although mathematical modelling is widely used in real estate valuation [32; 33; 34], it is rarely used to estimate other parameters of buildings other than value. [PERSON] et al. [26] demonstrated that the usable area of single-family houses with flat roofs can be precisely estimated using topographic data, neural networks, and regression analysis. Their study on 96 building designs from architectural offices and 29 existing buildings in Koszalin showed a high accuracy of estimating the usable area. The best neural network model, which was trained on building designs from design offices, was tested on real buildings in Koszalin. The estimation error was <9%, which can be considered a fairly good result. In a follow-up article [35] for residential buildings with a pitched roof based on data from architectural offices, it was shown that both linear regression and the neural network performed best when the input parameters were the building area, building height, number of floors, and knee wall height. The estimation error was 5% in the case of linear regression and 3% in the case of the neural network. For buildings built in different architectural styles between 2020 and 2022 in Koszalin that deviated significantly from the set from design offices, the accuracy of the best neural network estimate dropped to 15%. Similarly to [PERSON] et al. [26; 35], this article used two different datasets, namely architectural designs and existing buildings. The first justification is the fact that the designs from architectural offices contain full, detailed documentation of the building, in a known standard, which is not the case of existing buildings. Furthermore, a detailed description of the interior of the building and the structural solutions affecting the value of the usable area are known. Secondly, the existing data may contain measurement errors, which affects test quality. As the quality of linear and nonlinear models depends on the data quality, the use of precise architectural designs is a significant advantage. We have expanded our research to include residential buildings with multi-pitched roofs, which pose an additional challenge in estimating the usable area, due to the presence of slopes affecting the area of the top floor. Multi-pitched roofs are roofs that have more than two sloping planes that connect at different angles [36]. Multi-pitched roofs are used primarily for their functionality, aesthetics, and durability. They offer several advantages compared with single-pitch or gable roofs. The slopes effectively drain rainwater and snow, which reduces the risk of leaking and structural damage. Due to their complex structure, multi-pitched roofs are more likely to withstand strong winds and other extreme weather conditions. Their shape dissipates wind forces, which increases the stability of the building. The slopes allow the space under the roof to be used more efficiently, which allows for arrangement of additional rooms (e.g., attics). Multi-pitched roofs have a more complex form, which affects the attractiveness of the building. They are often used in villa-type designs and modern residences, where aesthetics play an important role. Furthermore, the larger roof area facilitates the design of adequate ventilation, which improves living comfort and affects structure durability. Disadvantages of multi-pitched roofs include a fairly complicated structure, which entails a higher price than flat or gable roofs. There are several types of multi-pitched roofs, such as hipped, tented, mansard, monitor, and many others. In this article, the hip and multi-slope roofs were primarily considered.