We consider a point P in the plane and reflect it across each side of a given polygon to obtain a symmetric polygon. This study investigates how the signed area of the symmetric polygon varies with the position of P, and analyzes the geometric structure of the corresponding equal-area loci. Our main results are summarized as follows. First, we show that any three non-collinear symmetric points uniquely determine the original triangle, establishing the reversibility of the symmetric construction. Second, we prove that the signed area satisfies an additive relation under a triangular decomposition of the polygon. Third, we show that for any polygon, the equal-area center exists and is unique, and we provide a straightedge-and-compass construction. Fourth, we derive explicit signed-area formulas for general quadrilaterals and give a complete discussion of special cases, including parallelograms, trapezoids, and cyclic quadrilaterals. Finally, we extend the results to general polygons and show that the signed area can be expressed as a linear combination of circle powers. As a consequence, the equal-area loci reduce to a single circle or degenerate into a family of parallel lines in special cases.