This page presents the preprint research paper “An Alternative Geometric Derivation of Triangle Area from Side Lengths” by Rudra Sangram Jadhav, hosted on Zenodo with DOI https://doi.org/10.5281/zenodo.16849119 . The paper introduces a step-by-step geometric derivation of a triangle area formula using only side lengths and the Pythagorean theorem.

We present an alternative geometric derivation of the triangle area formula expressed solely in terms of side lengths a, b, and c. Using elementary geometry and the Pythagorean theorem, we systematically derive the formula:

A =(1/4)√[(2ac)² − (a² + c² − b²)²].

This approach provides clear geometric intuition connecting basic geometric principles to triangle area calculations without requiring advanced mathematical tools. The derivation is accessible to high school and undergraduate students, offering pedagogical value by demonstrating how fundamental geometric relationships lead to practical area computation methods. While mathematically equivalent to Heron’s formula, this derivation emphasizes geometric reasoning over algebraic manipulation.

Keywords:- triangle area, Heron's formula, geometric derivation, Pythagorean theorem, preprint

@misc{jadhav2025triangle,

  author = {Rudra Sangram Jadhav},

  title = {An Alternative Geometric Derivation of Triangle Area from Side Lengths},

  howpublished = {Zenodo, DOI:10.5281/zenodo.16849119},

  year = {2025},

  note = {Preprint}

}