A Short Formula for the Area of a Quadrilateral with Two Equal Opposite Sides and it’s Application

Yordan Tabov 1), Stanislav Stefanov 2), Haim Haimov 3), Dobrinka Milusheva-Boykina 4)

1) Institute of Mathematics and Informatics, BAS – Sofia, Bulgaria
2) Todor Kableshkov University of Transport – Sofia, Bulgaria
4) University of Plovdiv “Paisii Hilendarski” – Plovdiv, Bulgaria

https://doi.org/10.53656/math2025-2-1-asf

Abstract. The article develops methods for solving complex problems at the level of mathematics olympiads, which are necessary for both high school students and their teachers. At the heart of these methods lies a formula for the area of a quadrilateral with a pair of equal but non-parallel opposite sides. It obtains as a special case of a more general formula for the area of an arbitrary convex quadrilateral, discussed in (Stefanov et al. 2024). Here we will prove the last formula in a more direct way and will consider its application to efficiently solving geometric problems.

Keywords: a special kind of quadrilaterals; area formulas; area of a parallelogram; problems

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