Area of Any Quadrilateral from Side Lengths

Alan Michael Gomez Calderon*
Pontificia Universidad Católica Madre y Maestra (PUCMM), Santiago de los Caballeros, Dominican Republic.
Periodicity:January - June'2025
DOI : https://doi.org/10.26634/jmat.14.1.21452

Abstract

In this paper we show that the area of any quadrilateral can be estimated from the four lengths sides. With the Triangle Inequality Theorem and a novel provided diagonal's formula, the boundaries of quadrilateral diagonals are found. Finally, Bretschneider's formula can be applied to find a set of possible areas.

Keywords

Area, Quadrilateral, Adjacent Triangle, Concave, Cosine Law.

How to Cite this Article?

Calderon, A. M. G. (2025). Area of Any Quadrilateral from Side Lengths. i-manager’s Journal on Mathematics, 14(1), 1-4. https://doi.org/10.26634/jmat.14.1.21452

References

[1]. Bretschneider, C. A. (1842). Untersuchung der trigonometrischen Relationen des geradlinigen Viereckes. Archiv der Mathematik, 2, 225-261.
[2]. Carnot, L. N. M., & Carnot, L. (1803). Géométrie de Position. Crapelet.
[3]. Dunham, W. (1990). Heron's formula for triangular area. Journey through Genius: The Great Theorems of Mathematics, 5, 113-132.
[4]. Sedrakyan, H., & Mozayeni, A. (2022). Formulas for Diagonals of any Quadrilateral. Mathematical Reflections.
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