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Nets and Surface Area
Students connect three-dimensional solids to two-dimensional nets and calculate total surface area.
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Beginner
15–20 minutes
Volume & Area
Volume & Area
Page 5 of 8
Inside Cover
Nets and Surface Area
At a Glance
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How does a two-dimensional net reveal the surface area of a solid?
Build Understanding
A net unfolds a solid into all of its faces. Surface area is the sum of the areas of those faces. Label congruent faces and dimensions before calculating.
For prisms, total surface area equals the two bases plus the lateral faces. For cylinders, the net contains two circles and one rectangle whose length is the circumference.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Identify every face in the net.
- Find each face area.
- Count congruent faces.
- Add all exposed surfaces.
- Use square units.
Click each word
Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Rectangular prism 3×4×5
1
SA=2(3×4)+2(3×5)+2(4×5)=94 square units.
Example 2
Triangular prism
1
Add two triangular bases and three rectangular lateral faces.
Ask and explain
Common Questions
Is surface area the same as volume? No.
Why is the cylinder rectangle length 2 pi r? It wraps around the base.
Do I include a missing or open face? Only if it is part of the surface.
Notice and correct
Common Misconceptions
Finding volume instead of surface area
Surface area covers faces and uses square units.
Omitting a face
Label every region on the net and pair congruent faces.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Find the surface area of a 2×3×6 rectangular prism.
2
We Do
Guided Practice
Cube side 4: SA=96 square units.
Rectangular prism 2x3x5: SA=62.
Cylinder r=3,h=8: SA=66 pi.
Triangular prism base triangle area 12, perimeter 18, length 7: SA=150.
Open-top 6x4x3 box: SA=84.
3
You Do
Independent Practice
Find the surface area of a 2×3×6 rectangular prism.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Create two rectangular prisms with equal volume but different surface areas. Determine which uses less packaging and explain why.
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Surface Area of Rectangular Prisms
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DeltaMath: Nets of Three-Dimensional Figures
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Open resource
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Before you begin, I can…
- I can identify the important information.
- I can use accurate notation, labels, and units.
- I can justify and verify my conclusion.
1
Question 1
What should happen before calculating?
2
Question 2
Which response gives the strongest evidence?
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Question 3
What is an effective accuracy check?
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Question 4
Why are units or labels important?
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What should a student do after finding an error?
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