What's the Area of Triangle Formed in Broken Stick Puzzle?

You Solved the broken stick problem and got the probability as 1/4! Let's dive deeper by calculating the expected area formed by the three pieces of the broken stick! Here you have the full derivation. Spoiler Alert - Average area of triangle is just PI/105! For Math nerds - Here's a challenge - can you find the probability of forming Acute triangle from the broken stick puzzle? Probability of forming triangle from broken stick- [   • Shorts  ] Probability of forming Acute / Obtuse triangles from broken stick- [   • The Broken Stick Problem: Acute vs Obtuse ...  ] About Barely Converging: Welcome to the home of high-level mathematics brought to life through elegant visual storytelling. I use programmatic animation (like Manim) to solve challenging math puzzles, break down probability riddles, and visualize rigorous proofs for IMO problems and math paradoxes. From the secrets of the Golden Ratio and geometric proofs to advanced calculus and quantitative interview prep, I translate abstract formulas into beautiful, satisfying visual solutions. If you are passionate about STEM, competitive math, or simply exploring the hidden patterns of the universe, subscribe for your regular dose of visually-driven mathematical exploration.