Grade 6 Math · Topic 59

Surface Area of Rectangular Prisms

Surface area is the total area of all the faces of a 3-D figure (the area of its net). A rectangular prism has 3 pairs of matching rectangular faces, so its surface area is twice the sum of those three face areas.

Lesson alignment: 6.G.A.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Unfold a rectangular prism

The net shows two faces of each dimension pair. Change the edge lengths and compare total surface area.

Think first: How many faces should appear when this solid is unfolded?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

A box is 5 × 3 × 2 cm. Find its surface area.

Start by writing the calculation clearly: ℓ w = 15, ℓ h = 10, w h = 6. Sum = 31. Double: SA = 2(31) = 62 cm².

Answer: 62 cm²

Worked example 2

A rectangular prism has ℓ = 8, w = 4, h = 6 in. Find SA.

Start by writing the calculation clearly: ℓ w = 32, ℓ h = 48, w h = 24. Sum = 104. SA = 2(104) = 208 in².

Answer: 208 in²

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. ℓ=3, w=2, h=4
    Check

    52

  2. ℓ=5, w=5, h=5
    Check

    150

  3. ℓ=6, w=4, h=3
    Check

    108

  4. ℓ=10, w=2, h=5
    Check

    160

  5. ℓ=7, w=3, h=2
    Check

    82

  6. ℓ=8, w=6, h=4
    Check

    208

  7. ℓ=9, w=5, h=3
    Check

    174

  8. ℓ=12, w=10, h=8
    Check

    592

Try this situation 1

A storage box is 10 in long, 6 in wide, and 4 in tall. How much wrapping paper covers it (surface area)?

Show a worked solution

Answer: 248 in².

Start by writing the calculation clearly: 2(10 · 6 + 10 · 4 + 6 · 4) = 2(60 + 40 + 24) = 2(124) = 248.

Try this situation 2

A cube has edge length 5 ft. Find its surface area.

Show a worked solution

Answer: 150 ft².

Start by writing the calculation clearly: SA = 6 s² = 6(25) = 150.

Fresh questions · saved on this device

Practice this skill

12 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A cube has an edge length of 6 centimeters. What is the surface area of the cube?

2. Marcus needs to paint all six faces of a wooden shipping crate that is 12 ft long, 7 ft wide, and 9 ft tall. How many square feet of paint will he need?

3. A cereal box has length 9 in, width 2.5 in, and height 12 in. What is its surface area?

4. An aquarium shaped like a rectangular prism is 30 cm long, 20 cm wide, and 25 cm tall. What is the total surface area of the aquarium (including the top)?

5. A rectangular storage box has length 8 cm, width 5 cm, and height 4 cm. What is the total surface area of the box?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗