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Unit 08 · Area Volume and Surface AreaLesson

Day 117Prism Surface Area

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

I can use a rectangular-prism net to find surface area.

01 · LEARN

Build the idea

A closed rectangular prism has two faces of area lw, two of lh, and two of wh. Add the six face areas: SA = 2lw + 2lh + 2wh. If a face is missing, do not include it.

WORKED EXAMPLE 1

A 6 cm by 2 cm base and 2 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

56 cm²

Closed surface area = 2(12+12+4) = 56.

WORKED EXAMPLE 2

A 7 cm by 5 cm base and 4 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

131 cm²

Closed surface area = 2(35+28+20) = 166. Remove the top area 35: 131.

02 · PRACTICE

Your turn

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

  1. A 8 cm by 4 cm base and 5 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  2. A 7 cm by 5 cm base and 6 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  3. A 2 cm by 5 cm base and 6 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  4. A 4 cm by 7 cm base and 4 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  5. A 8 cm by 4 cm base and 4 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  6. A 2 cm by 2 cm base and 2 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  7. A 4 cm by 6 cm base and 4 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

  8. A 6 cm by 6 cm base and 2 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

  9. A 7 cm by 7 cm base and 4 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

  10. A 8 cm by 5 cm base and 5 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 184 cm²

    Closed surface area = 2(32+40+20) = 184.

  2. 214 cm²

    Closed surface area = 2(35+42+30) = 214.

  3. 104 cm²

    Closed surface area = 2(10+12+30) = 104.

  4. 144 cm²

    Closed surface area = 2(28+16+28) = 144.

  5. 160 cm²

    Closed surface area = 2(32+32+16) = 160.

  6. 24 cm²

    Closed surface area = 2(4+4+4) = 24.

  7. 104 cm²

    Closed surface area = 2(24+16+24) = 128. Remove the top area 24: 104.

  8. 84 cm²

    Closed surface area = 2(36+12+12) = 120. Remove the top area 36: 84.

  9. 161 cm²

    Closed surface area = 2(49+28+28) = 210. Remove the top area 49: 161.

  10. 170 cm²

    Closed surface area = 2(40+40+25) = 210. Remove the top area 40: 170.

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