Resources/Surface area of 3D shapes
Grade 6•Printable worksheet + answer key•CC0 license

Surface area of 3D shapes

A printable lesson on finding the total area covering a solid.

Students learn to calculate surface area by adding the areas of all faces using SA = 2(lw + lh + wh).

Print-ready worksheet with answer key and quick teaching tips.

Grade 60 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free surface area worksheet for grade 6 builds understanding of 3D measurement and nets.

Lesson plan snapshot

15-20 min
  • Warm-up (3 min): unfold a box to see all six faces (net).
  • Model (5 min): identify face pairs and calculate areas.
  • Guided practice (5 min): complete problems 1-4 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: empty box to unfold, pencil, calculator

Learning targets

  • Understand surface area as the total area covering the outside of a 3D shape.
  • Identify the six faces of a rectangular prism.
  • Apply SA = 2(lw + lh + wh) to find surface area.
  • Solve word problems involving surface area.

Step-by-step approach

  1. 1Identify the length, width, and height.
  2. 2Find the area of each unique face: lw, lh, wh.
  3. 3Remember there are 2 of each face type.
  4. 4Add up all six faces: SA = 2(lw + lh + wh).
  5. 5Use square units (cm², m², in², ft²) for the answer.

Common mistakes

Mistake

Calculating volume instead of surface area.

Try instead

Surface area covers the OUTSIDE (square units). Volume fills the INSIDE (cubic units).

Mistake

Forgetting there are two of each face.

Try instead

A rectangular prism has 6 faces: 2 tops, 2 fronts, 2 sides. Multiply by 2.

Mistake

Using cubic units instead of square units.

Try instead

Surface area is measured in SQUARE units (²) because it's area.

Worked example

Guided
Find the surface area of a box that is 5 cm × 3 cm × 2 cm.
  1. Top/bottom faces: 5 × 3 = 15 cm² each, so 2 × 15 = 30 cm²
  2. Front/back faces: 5 × 2 = 10 cm² each, so 2 × 10 = 20 cm²
  3. Side faces: 3 × 2 = 6 cm² each, so 2 × 6 = 12 cm²
  4. Total: 30 + 20 + 12 = 62 cm²
Answer: 62 cm²

Related resources

Volume

Find the space inside 3D shapes.

View resource

Area & Perimeter

2D measurement foundations.

View resource

Practice problems

10 problems • 15 min

Printable worksheet
  1. 1
    Find the surface area of a cube with side length 5 cm.
  2. 2
    A gift box is 9 inches long, 8 inches wide, and 8 inches tall. How much wrapping paper is needed to cover the box (no overlap)?
  3. 3
    Find the surface area of a rectangular prism with length 8 cm, width 6 cm, and height 5 cm.
  4. 4
    A wooden block is 6 ft × 4 ft × 2 ft. How many square feet of paint is needed to cover all surfaces?
  5. 5
    Find the surface area of a cube with side length 7 cm.
  6. 6
    Find the surface area of a rectangular prism with length 5 cm, width 4 cm, and height 3 cm.
  7. 7
    A wooden block is 7 ft × 6 ft × 5 ft. How many square feet of paint is needed to cover all surfaces?
  8. 8
    Find the surface area of a rectangular prism with length 6 cm, width 2 cm, and height 5 cm.
  9. 9
    Find the surface area of a cube with side length 6 cm.
  10. 10
    Find the surface area of a cube with side length 2 cm.

Answer key

10 answers
  1. 11) 150 cm²
  2. 22) 416 square inches
  3. 33) 236 cm²
  4. 44) 88 sq ft
  5. 55) 294 cm²
  6. 66) 94 cm²
  7. 77) 214 sq ft
  8. 88) 104 cm²
  9. 99) 216 cm²
  10. 1010) 24 cm²

Teacher tips

  • TUnfold cereal boxes to show nets and identify faces.
  • TConnect to wrapping presents - how much paper do you need?
  • TCompare surface area and volume: which matters for wrapping vs filling?

Parent tips

  • PWrap a box together and talk about how much paper you need.
  • PAsk: 'If we painted this box, how much area would we paint?'
  • PFind boxes at home and have your child identify the six faces.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).