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Overview
Mathematics at Work 11
Measurement
1. Solve problems involving SI and imperial units in surface area measurements and verify solutions
1.3 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