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Unit 08 · Area Volume and Surface AreaLesson

Day 116Drawing and Labeling Nets

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

I can draw a net and account for every face of a solid.

01 · LEARN

Build the idea

A net unfolds all faces into a plane without overlap. Rectangular prisms have three matching pairs of rectangles. Pyramids have a polygonal base and triangular sides. Add face areas, not edge lengths.

WORKED EXAMPLE 1

Draw a net for a closed 3 × 4 × 5 cm rectangular prism. Label the six faces and calculate total area.

2 faces each of 3×4, 3×5, 4×5; 94 cm²

Add 2(12) + 2(15) + 2(20) = 94.

WORKED EXAMPLE 2

Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 5 cm. Label all faces and find surface area.

2 triangles (area 6 each), rectangles 3×5, 4×5, 5×5; SA 72 cm²

Triangle pair: 12 cm²; rectangles: (3+4+5) × 5 = 60; total 72.

02 · PRACTICE

Your turn

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

  1. Draw a net for a closed 5 × 5 × 4 cm rectangular prism. Label the six faces and calculate total area.

  2. Draw a net for a closed 3 × 3 × 2 cm rectangular prism. Label the six faces and calculate total area.

  3. Draw a net for a closed 7 × 3 × 3 cm rectangular prism. Label the six faces and calculate total area.

  4. Draw a net for a closed 2 × 4 × 3 cm rectangular prism. Label the six faces and calculate total area.

  5. Draw a net for a closed 2 × 2 × 4 cm rectangular prism. Label the six faces and calculate total area.

  6. Draw a net for a closed 6 × 7 × 2 cm rectangular prism. Label the six faces and calculate total area.

  7. Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 5 cm. Label all faces and find surface area.

  8. Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 4 cm. Label all faces and find surface area.

  9. Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 8 cm. Label all faces and find surface area.

  10. Draw a net for a triangular prism. Its two congruent right-triangle bases have legs 3 cm and 4 cm and hypotenuse 5 cm; prism length is 3 cm. Label all faces and find surface area.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 2 faces each of 5×5, 5×4, 5×4; 130 cm²

    Add 2(25) + 2(20) + 2(20) = 130.

  2. 2 faces each of 3×3, 3×2, 3×2; 42 cm²

    Add 2(9) + 2(6) + 2(6) = 42.

  3. 2 faces each of 7×3, 7×3, 3×3; 102 cm²

    Add 2(21) + 2(21) + 2(9) = 102.

  4. 2 faces each of 2×4, 2×3, 4×3; 52 cm²

    Add 2(8) + 2(6) + 2(12) = 52.

  5. 2 faces each of 2×2, 2×4, 2×4; 40 cm²

    Add 2(4) + 2(8) + 2(8) = 40.

  6. 2 faces each of 6×7, 6×2, 7×2; 136 cm²

    Add 2(42) + 2(12) + 2(14) = 136.

  7. 2 triangles (area 6 each), rectangles 3×5, 4×5, 5×5; SA 72 cm²

    Triangle pair: 12 cm²; rectangles: (3+4+5) × 5 = 60; total 72.

  8. 2 triangles (area 6 each), rectangles 3×4, 4×4, 5×4; SA 60 cm²

    Triangle pair: 12 cm²; rectangles: (3+4+5) × 4 = 48; total 60.

  9. 2 triangles (area 6 each), rectangles 3×8, 4×8, 5×8; SA 108 cm²

    Triangle pair: 12 cm²; rectangles: (3+4+5) × 8 = 96; total 108.

  10. 2 triangles (area 6 each), rectangles 3×3, 4×3, 5×3; SA 48 cm²

    Triangle pair: 12 cm²; rectangles: (3+4+5) × 3 = 36; total 48.

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