New Formula for the Area of a General Quadrilateral Using Opposite Sides and Four Angles

In this paper, we derive an explicit formula for the area of the particular quadrilaterals using only the lengths of a pair of opposite sides and the four interior angles. The formula is based on known geometric relationships and is presented after algebraic simplification and manipulation. Furthermore, we clarify the conditions under which the formula is valid and elucidate its geometric background. As a result, we demonstrate its applicability not only to convex and concave quadrilaterals but also to the particular self-intersecting quadrilaterals.