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Overview
Mathematics 11
Measurement
3. Understand relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D objects
3.2 Surface area and volume of pyramids
Surface Area of a Pyramid
The surface area of a square pyramid equals its base area plus its four triangular faces.
What You'll Learn
Surface area of a square pyramid: SA = base area + 4 triangular faces = s squared + 2sl.
Each triangular face has area one half times base times slant height.
Volume of any pyramid: V = one third times base area times height.
The slant height can be found from the vertical height using the Pythagorean theorem.
A pyramid holds one-third the volume of a prism with the same base and height.
What You'll Practice
1
Finding missing slanted sides using the Pythagorean theorem
2
Calculating surface area of square and rectangular pyramids
3
Computing pyramid volume using base area and height
4
Converting between units (millimeters to centimeters) before solving
Why This Matters
Understanding pyramid surface area and volume is essential for solving real-world problems in architecture, engineering, and design. These skills build your spatial reasoning and prepare you for advanced geometry, trigonometry, and calculus applications involving three-dimensional shapes.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Surface Area
Volume
Pyramids
Pythagorean Theorem
3D Geometry
Unit Conversion
Triangles
Rectangles
NS Curriculum Aligned