In the realm of Ghanaian politics, gerrymandering is a practice that involves political leaders strategically manipulating the boundaries of voting constituencies to serve their vested interests. This research seeks to address the challenge of gerrymandering in Ghana by introducing a novel mathematical approach, a modified Convex Hull algorithm. The data were collected from the Asunafo North constituency, and the study aims to provide a practical and effective solution to promote electoral fairness, transparency, and democratic integrity in the Ghanaian political system. We develop and implement a modified Convex Hull algorithm, which provides a more accurate and relevant measure of compactness than traditional compactness metrics. The evaluated electoral constituency exhibited reduced susceptibility to gerrymandering, resulting in more equitable representation and a fairer political landscape.