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Unit 08 · Area Volume and Surface AreaLesson

Day 118Pyramid Nets and Surface Area

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.4
LEARNING TARGET

I can find pyramid surface area from its triangular faces and base.

01 · LEARN

Build the idea

For a square pyramid, draw one square and four triangles. Each triangle has area base edge × face height / 2. The face height is measured on the triangular face, not vertically inside the solid.

WORKED EXAMPLE 1

A square pyramid has base edge 16 cm. Each triangular face has perpendicular face height 10 cm. Draw a net and calculate total surface area.

576 cm²

Base = 256; each triangle = 16 × 10 ÷ 2 = 80; add four triangles to get 576.

WORKED EXAMPLE 2

A square pyramid has base edge 6 cm. Each triangular face has perpendicular face height 9 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

144 cm²

Base = 36; each triangle = 6 × 9 ÷ 2 = 27; add four triangles to get 144.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. A square pyramid has base edge 6 cm. Each triangular face has perpendicular face height 5 cm. Draw a net and calculate total surface area.

  2. A square pyramid has base edge 4 cm. Each triangular face has perpendicular face height 8 cm. Draw a net and calculate total surface area.

  3. A square pyramid has base edge 4 cm. Each triangular face has perpendicular face height 6 cm. Draw a net and calculate total surface area.

  4. A square pyramid has base edge 10 cm. Each triangular face has perpendicular face height 9 cm. Draw a net and calculate total surface area.

  5. A square pyramid has base edge 14 cm. Each triangular face has perpendicular face height 13 cm. Draw a net and calculate total surface area.

  6. A square pyramid has base edge 6 cm. Each triangular face has perpendicular face height 8 cm. Draw a net and calculate total surface area.

  7. A square pyramid has base edge 12 cm. Each triangular face has perpendicular face height 8 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

  8. A square pyramid has base edge 12 cm. Each triangular face has perpendicular face height 9 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

  9. A square pyramid has base edge 10 cm. Each triangular face has perpendicular face height 10 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

  10. A square pyramid has base edge 14 cm. Each triangular face has perpendicular face height 13 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 96 cm²

    Base = 36; each triangle = 6 × 5 ÷ 2 = 15; add four triangles to get 96.

  2. 80 cm²

    Base = 16; each triangle = 4 × 8 ÷ 2 = 16; add four triangles to get 80.

  3. 64 cm²

    Base = 16; each triangle = 4 × 6 ÷ 2 = 12; add four triangles to get 64.

  4. 280 cm²

    Base = 100; each triangle = 10 × 9 ÷ 2 = 45; add four triangles to get 280.

  5. 560 cm²

    Base = 196; each triangle = 14 × 13 ÷ 2 = 91; add four triangles to get 560.

  6. 132 cm²

    Base = 36; each triangle = 6 × 8 ÷ 2 = 24; add four triangles to get 132.

  7. 336 cm²

    Base = 144; each triangle = 12 × 8 ÷ 2 = 48; add four triangles to get 336.

  8. 360 cm²

    Base = 144; each triangle = 12 × 9 ÷ 2 = 54; add four triangles to get 360.

  9. 300 cm²

    Base = 100; each triangle = 10 × 10 ÷ 2 = 50; add four triangles to get 300.

  10. 560 cm²

    Base = 196; each triangle = 14 × 13 ÷ 2 = 91; add four triangles to get 560.

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