Pre-Algebra
Geometry
Surface area using nets
20 practice questions
0 video lessons
Theory + worked examples
Surface Area Using Nets
California Pre-Algebra • Standard 6.G.4 • Geometry
Surface Area Using Nets is a topic in Geometry in the California Common Core State Standards. It is aligned to Standard 6.G.4, which requires students to find surface area using nets of three-dimensional figures.
A net unfolds a solid into flat faces; the surface area is the sum of all the face areas.
Theory
A net unfolds a solid into its flat faces; the surface area is the total area of all the faces.
Add every face: a cube has \(6s^2\), a rectangular prism \(2(lw+lh+wh)\).
A net of a cube.
Surface area formulas.
Surface area:
\[\text{SA}=\text{sum of face areas}\]
A net makes every face visible.
How to find surface area
- Unfold the solid into a net.
- Find the area of each face.
- Add all the face areas.
- Label in square units.
Example 1 — Cube
Find the surface area of a cube with side \(3\).
Solution
Six faces of \(3^2\).
| \(6\cdot3^2\) | \(=\) | \(54\) |
Example 2 — Rectangular prism
Find the SA of a \(2\times3\times4\) prism.
Solution
Add all face pairs.
| \(2(6+8+12)\) | \(=\) | \(52\) |
Example 3 — Count faces
How many faces does a rectangular prism have?
Solution
Three pairs — six faces.
Example 4 — Why nets
Why use a net for surface area?
Solution
It shows every face flat, so you can add their areas.
Common pitfalls
Count every face — six for a prism.
Surface area is squared units, not cubed.
Opposite faces match in a prism.
Frequently asked questions
What is a net?
A flattened-out version of a solid's faces.
What is surface area?
The total area of all faces.
What is a cube's surface area?
\(6s^2\).
How many faces does a prism have?
Six.
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Area of triangles, quadrilaterals and polygons
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Volume of prisms and pyramids
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