Calculating the Area of a Triangle Given Three Vertices

The Organic Chemistry Tutor

This instructional math video provides a step-by-step tutorial on calculating the area of a triangle when given the coordinates of its three vertices. The video begins by plotting three specific points on a coordinate plane to visualize the triangle, establishing a geometric context for the algebraic work that follows. It bridges the gap between visual graphing and algebraic calculation, demonstrating how coordinate geometry allows for precise measurements without measuring tools. The core of the video focuses on a specific algebraic formula involving the absolute value of the sum and difference of coordinate products (often recognized as the "Shoelace Formula" or Surveyor's Formula). The narrator methodically assigns variables to the coordinates (x1, y1, etc.), substitutes these values into the formula, and performs the arithmetic operations. Key themes include coordinate geometry, substitution, order of operations with integers, and the interpretation of absolute value in the context of area. For educators, this video serves as an excellent resource for high school Geometry or Algebra 2 classes. It offers a procedural alternative to more cumbersome methods like the "box method" (enclosing the triangle in a rectangle) or using the distance formula combined with Heron's formula. Teachers can use this to introduce the concept of determinant-based area formulas, reinforce skills in evaluating expressions with negative numbers, or verify results obtained through graphing methods.