What if you could calculate the area of a triangle or the volume of a pyramid using just vectors? In this video, we show how linear algebra offers elegant solutions through a powerful concept called the determinant. You'll see how the formula |ad - bc| / 2 gives the area of a triangle, how this extends to volume in 3D, and why the determinant tells us so much more—including whether a matrix is invertible. Perfect for anyone curious about the real meaning of determinants—beyond just memorizing formulas. 📐 Topics covered: – Area from vectors – Volume of pyramids – Determinants as transformation scalars – Invertibility and linear independence 3 Blue 1 Brown Determinants: Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?” Instagram: Twitter/X: Facebook: Email: MathTheWorld@ Created by Doug Corey Script: Doug Corey and Jennifer Canizales Audio: Doug Corey Animation: Jennifer Canizales Music: Coma Media © 2025 BYU