Neft Teacher · Learn It

Unit 5 · Standard 6.GR.4

Represent Three-Dimensional Figures in Two Dimensions

Lesson 5-6 · Learn It — how the math works

Why we're learning this

Your class is designing custom wrapping paper for time capsule boxes. To figure out how much paper you need, you have to find the total surface area of each box. The trick? Unfold the box into a net so you can see every face laid flat! One time capsule box is 6 inches long, 4 inches wide, and 2 inches tall. How much wrapping paper covers the whole box?

✱ Math Workbench

Learn It

How do we find the surface area of a box?

Surface area is the total area of all the flat faces of a solid. A net unfolds the box flat so you can see and add all 6 faces. The answer uses square units.

Picture itSee what the math looks like before you read about it

Yuzuki is making paper replicas of the Pyramids of Giza for a social studies project. She has flat sheets of paper and needs to know how much paper each pyramid will take.
Where you see this in real lifeYuzuki is making paper replicas of the Pyramids of Giza for a social studies project. She has flat sheets of paper and needs to know how much paper each pyramid will take.

Watch me solve itI do — read one step at a time

The problem looks like this
Net of a box 8 in. long, 5 in. wide and 3 in. tall: three pairs of faces, 8 × 5, 8 × 3 and 5 × 3.8 in.5 in.3 in.
  1. My box is 8 in. long, 5 in. wide, and 3 in. tall. I unfold it into a and see 3 pairs of .
  2. Top and bottom: each is 8 × 5 = 40, and there are 2 of them, so 2 × 40 = 80.8 × 5 = 40
  3. Front and back: each is 8 × 3 = 24, so 2 × 24 = 48.8 × 3 = 24
  4. Left and right: each is 5 × 3 = 15, so 2 × 15 = 30.5 × 3 = 15
  5. I add all the pairs: 80 + 48 + 30 = 158. The is 158 in².80 + 48 + 30 = 158

Watch out — mistakes students make here

  • 135 is the volume — surface area adds up all six faces.
  • Surface area is measured in square units (in²), not cubic.
  • Square the edge length for one face's area first, then multiply by the number of faces.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now a smaller box: 4 long, 3 wide, 2 tall. How many pairs of does it have?
  2. Top and bottom: 4 × 3 = 12, times 2 = 24. Front and back: 4 × 2 = 8, times 2 = 16.4 × 3 = 12
  3. Left and right: 3 × 2 = 6, times 2 = 12. Now add 24 + 16 + 12. What is the ?3 × 2 = 6
  4. Yes, SA = 52 in². Remember to use square units.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table below, find the area of each pair, then add them for the total .
  • Write your answers in square inches (in²).

Solve: Find the of each time capsule box using its .

BoxLengthWidthHeightSurface Area
Box A10 in6 in4 in
Box B7 cm7 cm3 cm
Box C12 ft5 ft2 ft

Stuck? Open one hint at a time.

Hint 1

Each row needs SURFACE AREA, not volume — the total area of all six faces, in square units.

Hint 2

Use SA = 2lw + 2lh + 2wh for each row: three face areas, each doubled, then added together.

Hint 3

Box A: the faces are 10×6 = 60, 10×4 = 40, and 6×4 = 24. Double each one, then add the results.

Check my answer
✅ Answers:
  • Box A → Surface Area: 248 in²
  • Box B → Surface Area: 182 cm²
  • Box C → Surface Area: 188 ft²
Surface area adds all six faces, so use SA = 2lw + 2lh + 2wh in every row. Box A: 2(60) + 2(40) + 2(24) = 248 in². Box B: 2(49) + 2(21) + 2(21) = 182 cm². Box C: 2(60) + 2(24) + 2(10) = 188 ft². The answers carry square units because you are covering the outside, not filling the inside.

Turn & TalkSay it out loud with a partner

To find how much wrapping paper a time capsule box needs, why is unfolding it into a more helpful than looking at the 3D box?

Try starting with:

  • A net helps because it shows all ___ faces laid ___.Una red ayuda porque muestra las ___ caras puestas ___.
  • On the 3D box some faces are ___, but the net makes them all ___.En la caja 3D algunas caras están ___, pero la red las hace todas ___.
Use these wordssurface areanetfacetwo-dimensionaledge