Explore a novel approach to calculating the area of a triangle using only the lengths of its sides in this 38-minute lecture. Learn about Archimedes' ancient problem and discover a more elegant solution based on Rational Trigonometry. Delve into the two most fundamental formulas in mathematics: Pythagoras' theorem and the Triple quad formula. Understand how this method improves upon Heron's formula by eliminating unnecessary irrationalities. Follow along as the lecturer demonstrates the solution with a practical example and provides a proof. Conclude with an intriguing application of this concept to relativistic physics.