A researcher embarks on the development of an intelligent system capable of detecting the movement of chess pieces, drawing upon the knowledge of the digital electronic module she acquired during her course. The project involves the integration of algorithms, digital logic design, and sensor technologies to create a system that can recognize the unique characteristics of each chess piece and comprehend its precise movements on the chessboard. To achieve this, the researcher is studying various rectangle orientations, and the number of these orientations found on the chessboard is recorded in a table. A rectangle on the chessboard is uniquely determined by a pair of vertical and horizontal lines. The bounding lines are represented as vertical x horizontal, where both rectangle orientations, such as $(1$ x $2)$ or $(2$ x $1),$ yield the same surface area for the rectangle. However, she computed incorrectly and made a few errors while tabulating the total numbers for these rectangle orientations in the table.