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Surface area and nets worksheet

Grade 6 math, Common Core 6.G.A.4. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Surface area and nets

Grade 6 math, Common Core 6.G.A.4

Find the surface area. Include the units.

  1. 1.
    A net has six rectangles: two that are 6 by 9 ft, two that are 6 by 10 ft and two that are 9 by 10 ft.
  2. 2.
    A cube has edges 10 ft long.
  3. 3.
    A net has six rectangles: two that are 3 by 5 cm, two that are 3 by 7 cm and two that are 5 by 7 cm.
  4. 4.
    A triangular prism has right-triangle ends with sides 9, 12 and 15 m, and is 5 m long.
  5. 5.
    A rectangular prism is 5 in long, 9 in wide and 7 in tall.
  6. 6.
    A cube has edges 3 in long.
  7. 7.
    A rectangular prism is 10 ft long, 2 ft wide and 6 ft tall.
  8. 8.
    A cube has edges 2 m long.
  9. 9.
    A net has six rectangles: two that are 2 by 4 m, two that are 2 by 7 m and two that are 4 by 7 m.
  10. 10.
    A net has six rectangles: two that are 3 by 6 in, two that are 3 by 7 in and two that are 6 by 7 in.
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Surface area and nets

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 408 ft²

    2(54) + 2(60) + 2(90) = 408

  2. 2. 600 ft²

    6 faces × 10² = 6 × 100 = 600

  3. 3. 142 cm²

    2(15) + 2(21) + 2(35) = 142

  4. 4. 288 m²

    Two triangles: 2 × 12 × 9 × 12 = 108Three rectangles: (9 + 12 + 15) × 5 = 180Total: 288

  5. 5. 286 in²

    2(5 × 9) + 2(5 × 7) + 2(9 × 7)= 90 + 70 + 126 = 286

  6. 6. 54 in²

    6 faces × 3² = 6 × 9 = 54

  7. 7. 184 ft²

    2(10 × 2) + 2(10 × 6) + 2(2 × 6)= 40 + 120 + 24 = 184

  8. 8. 24 m²

    6 faces × 2² = 6 × 4 = 24

  9. 9. 100 m²

    2(8) + 2(14) + 2(28) = 100

  10. 10. 162 in²

    2(18) + 2(21) + 2(42) = 162

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About surface area and nets

Surface area is the total area of all the faces of a 3D shape, like the amount of wrapping paper needed to cover a box. A net is the shape unfolded flat. For a rectangular prism, find the area of each pair of matching faces: SA = 2lw + 2lh + 2wh.

Worked example 1

A cube has edges 11 cm long.
  1. Step 1.6 faces × 11² = 6 × 121 = 726

Answer: 726 cm²

Worked example 2

A triangular prism has right-triangle ends with sides 6, 8 and 10 ft, and is 12 ft long.
  1. Step 1.Two triangles: 2 × 12 × 6 × 8 = 48
  2. Step 2.Three rectangles: (6 + 8 + 10) × 12 = 288
  3. Step 3.Total: 336

Answer: 336 ft²

Worked example 3

A rectangular prism is 4 ft long, 5 ft wide and 4 ft tall.
  1. Step 1.2(4 × 5) + 2(4 × 4) + 2(5 × 4)
  2. Step 2.= 40 + 32 + 40 = 112

Answer: 112 ft²

Watch out for

  • A rectangular prism has 6 faces in 3 matching pairs.
  • Surface area is in square units, because it is an area.
  • Sketch the net and label each face with its length and width so you don’t miss one.

Practice surface area and nets online

On StudyWiz, your kid can practice surface area and nets with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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