Why is Area = r × s?

In this video from Phymics, we visualize the beautiful derivation of the Inradius formula for a scalene triangle using the "Area Summation Method. "We break down the proof step-by-step: Constructing the Incenter (I): See how the angle bisectors meet to form the center of the circle. The Geometry: Understanding why the radii are perpendicular heights. Partitioning: Splitting the scalene triangle into three smaller triangles. The Algebra: Summing the areas to derive the famous formula. This visual proof makes the math intuitive and easy to remember. Perfect for geometry students, math enthusiasts, and anyone who loves visual learning! Timestamps: 0:00 - Introduction to the Scalene Triangle 0:10 - The Incenter & Incircle 0:35 - The "Aha!" Moment: Splitting the Triangle 1:05 - Summing the Areas 1:40 - The Semiperimeter (s) 2:00 - The Final Formula Tools used: Python (Manim Library) for animations. Subscribe to Phymics for more visual physics and mathematics explanations! #Geometry #MathVisualized #Manim #Inradius #TriangleProperties #Phymics #VisualProof #MathEd