Grade 6 Math · Topic 61

Surface Area of Pyramids

A pyramid has one polygon base and triangular faces that meet at a single point (the apex). For a square pyramid, the surface area is the base's area plus the total area of the four triangular faces.

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

Explore visually

Unfold a square pyramid

The net contains one square base and four congruent triangular faces.

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.

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Follow the worked examples

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

Worked example 1

A square pyramid has s = 6 cm and slant height ℓ = 5 cm. Find SA.

Base: 6² = 36. Triangles: 4 · 1/2(6)(5) = 60. SA = 36 + 60 = 96 cm².

Answer: 96 cm²

Worked example 2

A square pyramid has s = 10 in, ℓ = 8 in. Find SA.

Start by writing the calculation clearly: 10² = 100. Triangles: 4 · 1/2(10)(8) = 160. SA = 100 + 160 = 260 in².

Answer: 260 in²

Try a few on your own

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

  1. s=4, ℓ=5
    Check

    56

  2. s=5, ℓ=6
    Check

    85

  3. s=8, ℓ=7
    Check

    176

  4. s=3, ℓ=4
    Check

    33

  5. s=12, ℓ=10
    Check

    384

  6. s=6, ℓ=9
    Check

    144

  7. s=9, ℓ=11
    Check

    279

  8. s=7, ℓ=8
    Check

    161

Try this situation 1

A glass pyramid paperweight has a 4 in square base and slant height 6 in. Find its surface area.

Show a worked solution

Answer: 64 in².

Start by writing the calculation clearly: 4² + 4 · 1/2(4)(6) = 16 + 48 = 64.

Try this situation 2

A tent shaped like a square pyramid has s = 8 ft and ℓ = 5 ft. How much fabric is needed (sides only, no base)?

Show a worked solution

Answer: 80 ft².

Sides only: 4 · 1/2(8)(5) = 80.

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.

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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 square pyramid has a square base with side length 8 cm. Each triangular face has a slant height of 10 cm. What is the total surface area of the pyramid?

2. A square pyramid with base side 10 cm has a surface area of 340 cm². What is the slant height?

3. A square pyramid has a base side of 5 m and a slant height of 8 m. What is the total surface area?

4. A square pyramid has a base side length of 6 m and a slant height of 7 m. Which expression correctly calculates the surface area?

5. A rectangular pyramid has a rectangular base 12 cm by 8 cm and a slant height of 10 cm. All four triangular faces have the same slant height. What is the surface area?

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.

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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 ↗