en Architectural Engineering Architectural Engineering Research Paper Research Paper <span style="font-size:10pt"><span new="" roman="" style="font-family:" times=""><span data-darkreader-inline-color="" style="color: black; --darkreader-inline-color: #e8e6e3;"><i><span style="font-size:11.0pt">The physical-geometric characteristics of buildings have a very important role in the regulation of microclimate conditions and the thermal situation of interior and exterior spaces of buildings. This research aims to investigate the amount of received direct radiation energy of vertical surfaces in buildings and determine the appropriate form, aspect ratio, and orientation of buildings in the cities of Ardabil, Tabriz, Sanandaj, and Hamedan in the Northwest of Iran with cold climate. For this purpose, six polygonal forms (with the same floor area and height) including square, rectangle, hexagon, octagon, hexadecagon (16-sided), and triacontadigon (32-sided) were selected to be examined. Afterward, the specified optimal form(rectangle) was surveyed with the aspect ratios of 1:1.2, 1:1.4, 1:1.6, 1:1.8, 1:2 and in the orientations of 180&ordm;, 165&ordm;, 150&ordm;, 135&ordm;, 120&ordm;, 105&ordm; SE and SW. Using the &ldquo;Law of Cosines&rdquo; computational method, the amount of received direct energy on vertical surfaces has been calculated and processed, for different months and during the cold and hot periods of the year. The results of the research show that the appropriate form of the buildings in the studied cities is a rectangle with an east-west orientation. The most suitable aspect ratio for the rectangular form with east-west orientation in the cities of Ardabil, Tabriz, Sanandaj, and Hamedan is 1:1.2. The appropriate orientation for the determined aspect ratio in the studied cities is 165&deg; Southeast.</span></i></span></span></span><br> &nbsp; Optimal form, Aspect ratio, Building orientation, Cold climate, Solar energy 44 55 http://ijaup.iust.ac.ir/browse.php?a_code=A-11-1840-1&slc_lang=en&sid=1 Hassan Akbari h.akbari.arc@gmail.com 180031947532846005968 180031947532846005968 Yes Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran Fatemeh Sadat Hosseini Nezhad Hosseininezhad1359@gmail.com 180031947532846005969 180031947532846005969 No Shahid Beheshti University