How to Find the Volume and Surface Area of Pyramids

The Organic Chemistry Tutor

This comprehensive math tutorial guides students through the process of calculating the volume and surface area for both square-based and triangular pyramids. The video breaks down complex geometric concepts into clear, manageable steps, starting with basic volume formulas and progressing to more advanced surface area calculations that require finding the slant height. Through a series of hand-drawn diagrams and step-by-step practice problems, viewers learn how to distinguish between the actual height and slant height of a pyramid—a common source of confusion for students. The video explores key themes in geometry, including the application of the Pythagorean theorem to find missing dimensions in 3D shapes. It covers the specific formulas for square and equilateral triangular bases, demonstrating how lateral area is derived from the sum of the triangular faces. The instructor uses multiple examples with varying known variables (e.g., being given height vs. slant height) to ensure students are prepared for different types of problem scenarios they might encounter in exams. For educators, this video serves as an excellent instructional tool for 7th through 10th-grade geometry units. It addresses specific misconceptions, such as confusing base height with pyramid height, and provides natural pause points for students to attempt calculations independently. The visual demonstration of breaking down surface area into "base plus lateral area" helps students conceptually understand the formulas rather than just memorizing them, promoting deeper mathematical reasoning.