# Linear and Nonlinear Modelling of the Usable Area of Buildings with Multi-Pitched Roofs
A lack of full compliance between older standards and new regulations can lead to differences in the interpretation and results of property appraisal. The errors can range from a few to several percent, depending on the architecture of the building and the standard used. A detailed description of the norms and differences between standards can be found in the literature [26; 27]. In this article, estimates of the usable area of detached residential buildings with multi-pitched roofs were conducted in accordance with the PN-ISO 9836:2015-12 standard. The PN-ISO 9836:2015-12 standard introduced new rules for calculating the usable area (especially in buildings with multi-pitched roofs) considering the slope of the roofs. According to these regulations, 100% of the area with a height > 2.2 m is included in the usable area; 50% of the area with a height between 1.4 and 2.2 m and areas < 1.4 m are excluded. An important consequence of this regulation is also the complete omission of partition walls, in contrast to the previous standards. There is another publicly available source of data, the Database of Topographic Objects (hereafter referred to as BDOT10k) [28] that supports estimating the usable area of buildings. BDOT10k is a spatial database containing information about the topography of Poland. It collects detailed data on various landscape features, such as buildings, roads, rivers, forests, and railways, along with their descriptive attributes and location. The descriptions of the buildings in the database include features such as height, width, length, and perimeter. The main applications of BDOT10k are in spatial planning, environmental protection, real estate management, and technical infrastructure management. Users represent both the public administration and the private sector. This database provides accurate, unified data that is extremely useful for various types of spatial analysis, including building surface modelling and other geoinformation analysis. The information contained in BDOT10k comes from several sources, including airborne Light Detection and Ranging (LiDAR) scanning. Airborne LiDAR scanning is a remote sensing technique used to obtain precise information about the Earth's surface, terrain objects, and more. LiDAR scanning involves the emission of laser pulses from a device mounted on an aircraft or drone, which bounce off the surface of the earth, buildings, trees, and other objects and then return to the sensor. Based on the return time of the pulses and the measured angle, the height and structure of the objects can be determined with high precision. In Poland, LiDAR data are provided by the Information System of the National Guard Program against Extraordinary Threats [29; 30]. LiDAR scanning was carried out in Poland at two levels of detail (LoD): LoD1 and LoD2. The LoD1 level contains a square grid of measurement points with a density of 4 points/m\({}^{2}\), omits the geometry of the roof and contains only building blocks. The LoD2 level is characterized by a rectangular grid of measurement points, with a grid density of 12 points/m\({}^{2}\), containing roof structures and simple additional building textures, such as extensions or garages. Most of the LiDAR surface data in Poland shows the accuracy of LoD2, but the residential buildings analyzed in this article and located in Koszalin show the accuracy of LoD1, therefore they cannot be used to estimate the height of a building. The BDOT10k database is available in the Geoportal database managed by the Head Office of Geodesy and Cartography. Information for the city of Koszalin can been downloaded from the Geoportal in the CityGML 2.0 standard [31]. The information was accessed using QGIS Desktop v. 3.28.2. Google Street View was used when the REPR lacked information about the number of floors. Additionally, the data in the article come from notifications on the completion of the construction of residential buildings in Koszalin, sent to the District Inspector of Building Supervision in Koszalin.