Grade 6 · Math · Lesson 21

Surface Area of Prisms and Pyramids

Surface area is the total area of every flat face on the outside of a 3D solid. Imagine unfolding a cardboard box flat onto a table: every panel you see is a face, and the sum of those face areas is the surface area. Surface area answers questions like how much wrapping paper, how much paint, or how much sheet metal you need to cover a solid. The formulas are identical whether the measurements are US customary (sq inches, sq feet) or metric (cm^2, m^2) — only the unit labels change. For prisms and pyramids, every face is a rectangle, square, or triangle, so once you can find those three areas you can find any surface area.

What this lesson teaches

1Calculate the surface area of rectangular prisms using SA = 2lw + 2lh + 2wh in sq inches or cm^2
2Calculate the surface area of cubes using SA = 6s^2 in either US customary or metric units
3Calculate the surface area of triangular prisms by adding the two triangles and three rectangles
4Solve real-world surface area problems in both customary (sq in, sq ft) and metric (cm^2, m^2)

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