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Measures and solids · Ages 13–14

Surface area of a prism worksheet

Part of: Prisms & cylinders

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Surface area of a prism worksheet

Measures and solids · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

Part A: Working out and filling in (2 marks each)

  1. 1.The prism in the picture has a right-angled triangle with sides 6 cm, 8 cm and 10 cm as its cross-section, and is 6 cm long. What is its total surface area, in cm²?

    Answer:

  2. 2.The cuboid in the picture is 9 cm long, 6 cm wide and 8 cm high. What is its total surface area, in cm²?

    Answer:

  3. 3.The prism in the picture has a trapezium as its cross-section, 9 cm along the top and 21 cm along the bottom, each slanting side 10 cm; it is 6 cm long. What is the area of all its sides together, in cm²?

    Answer:

  4. 4.The prism in the picture has an isosceles triangle as its cross-section: 18 cm across, 12 cm high, its two equal sides 15 cm each; the prism is 15 cm long. What is its total surface area, in cm²?

    Answer:

  5. 5.The prism in the picture is 7 cm long, its cross-section a right-angled triangle of sides 4 cm, 3 cm and 5 cm. The two ends make cm², the three sides cm², the total surface area cm².

    Fill in each blank

    Answer:

  6. 6.The prism in the picture has a trapezium as its cross-section, 3 cm along the top and 15 cm along the bottom, each slanting side 10 cm; it is 13 cm long. What is the area of all its sides together, in cm²?

    Answer:

  7. 7.The prism in the picture has an isosceles triangle as its cross-section: 6 cm across, 4 cm high, its two equal sides 5 cm each; the prism is 6 cm long. What is its total surface area, in cm²?

    Answer:

  8. 8.The prism in the picture has a right-angled triangle with sides 6 cm, 8 cm and 10 cm as its cross-section, and a total surface area of 288 cm². How long is it?

    Answer:

  9. 9.The prism in the picture has an L-shaped cross-section, 12 cm wide and 10 cm high, both arms 3 cm thick; it is 11 cm long. What is its total surface area, in cm²?

    Answer:

  10. 10.The prism in the picture has an L-shaped cross-section, 12 cm wide and 12 cm high, both arms 4 cm thick; it is 7 cm long. What is its total surface area, in cm²?

    Answer:

Part B: Choose, or true or false (2 marks each)

  1. 11.Open out the three sides of the prism in the picture and they join into one rectangle, 18 cm wide. How long is the rectangle?

    • A. 40 cm
    • B. 60 cm
    • C. 58 cm
    • D. 23 cm

    Choose the right answer

    Answer:

  2. 12.A prism's cross-section has an area of 19 cm² and a perimeter of 18 cm, and the prism is 10 cm long. Its total surface area is 199 cm².

    True or false?

    Answer:

Part C: Word problems (4 marks each)

  1. 13.An open-topped cuboid box is to be made from thin board, its bottom 28 cm by 18 cm and its sides 15 cm high. At least how much board does it take?

    • A. 1884 cm²
    • B. 2388 cm²
    • C. 1698 cm²
    • D. 1194 cm²

    Choose the right answer

    Working:

    Answer:

  2. 14.A box is a triangular prism, its cross-section a right-angled triangle of sides 12 cm, 16 cm and 20 cm, and it is 22 cm long. The card it is made of costs $0.5 for each 100 cm². How many dollars of card does one box take?

    Working:

    Answer:

  3. 15.The tent in the picture has isosceles triangles at its ends: 240 cm across, 160 cm high, each slanting side 200 cm; the tent is 160 cm long. It has no floor sheet: its ends and two slanting sides are canvas. How many cm² of canvas does it take?

    Working:

    Answer:

  4. 16.A cuboid gift box is 26 cm long, 20 cm wide and 12 cm high. How many cm² of wrapping paper cover the whole box exactly (no overlaps)?

    Working:

    Answer:

  5. 17.A metal trough with no lid is 36 cm long, its cross-section a trapezium: 17 cm across the open top, 11 cm across the bottom, 4 cm deep, each slanting side 5 cm. The two ends take cm² of metal, the bottom and the two sides cm², the whole trough cm².

    Fill in each blank

    Working:

    Answer:

  6. 18.Find the total surface area of a prism whose cross-section is a right-angled triangle of sides 7 cm, 24 cm and 25 cm, 8 cm long. Put the steps in order.

    • A. Total = 448 + 2 × 7 × 24 ÷ 2 = 616
    • B. Sides = 56 × 8 = 448
    • C. Perimeter = 7 + 24 + 25 = 56

    Write the letters in the right order

    Working:

    Answer:

Show the answers and working

Surface area of a prism worksheet: Answers and working

Part A: Working out and filling in

  1. 1. 192 cm²

    The two ends 2 × (6 × 8 ÷ 2) = 48, the sides = perimeter × length = 24 × 6 = 144; 192 cm² in all.

  2. 2. 348 cm²

    Three pairs of equal faces: 2 × (48 + 54 + 72) = 348 cm².

  3. 3. 300 cm²

    The sides open into one rectangle: the perimeter 9 + 21 + 10 + 10 = 50 cm, times the length 6: 300 cm².

  4. 4. 936 cm²

    The ends 2 × (18 × 12 ÷ 2) = 216; perimeter 18 + 15 + 15 = 48, sides 48 × 15 = 720; 936 cm² in all.

  5. 5. 12, 84, 96

    Ends 2 × 4 × 3 ÷ 2 = 12; sides (4 + 3 + 5) × 7 = 84; 96 in all.

  6. 6. 494 cm²

    The sides open into one rectangle: the perimeter 3 + 15 + 10 + 10 = 38 cm, times the length 13: 494 cm².

  7. 7. 120 cm²

    The ends 2 × (6 × 4 ÷ 2) = 24; perimeter 6 + 5 + 5 = 16, sides 16 × 6 = 96; 120 cm² in all.

  8. 8. 10 cm

    The ends are 2 × 6 × 8 ÷ 2 = 48, so the sides are 288 − 48 = 240; the perimeter is 24 cm, so the length = 240 ÷ 24 = 10 cm.

  9. 9. 598 cm²

    The cross-section is 57 cm², two of them 114; the L's perimeter is the same as a 12 by 10 rectangle's, 2 × (12 + 10) = 44, so the sides are 44 × 11 = 484; 598 cm² in all.

  10. 10. 496 cm²

    The cross-section is 80 cm², two of them 160; the L's perimeter is the same as a 12 by 12 rectangle's, 2 × (12 + 12) = 48, so the sides are 48 × 7 = 336; 496 cm² in all.

Part B: Choose, or true or false

  1. 11. A. 40 cm

    The three sides laid end to end make the cross-section's perimeter: 15 + 8 + 17 = 40 cm.

  2. 12. False

    Total surface area = 2 × cross-section + perimeter × length = 2 × 19 + 18 × 10 = 218 cm².

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

  1. 13. A. 1884 cm²

    One bottom, 28 × 18, and four sides, 2 × 18 × 15 + 2 × 28 × 15: 1884 cm².

  2. 14. 6.24 dollars

    Total surface area 2 × 12 × 16 ÷ 2 + (12 + 16 + 20) × 22 = 1248 cm², and 1248 ÷ 100 × 0.5 = $6.24.

  3. 15. 102400 cm²

    Ends 2 × (240 × 160 ÷ 2) = 38400; the two slopes 2 × 200 × 160 = 64000; no floor, so the bottom isn't counted: 102400 cm².

  4. 16. 2144 cm²

    Six faces, three pairs: 2 × (26 × 20 + 20 × 12 + 26 × 12) = 2144 cm².

  5. 17. 112, 756, 868

    The ends: 2 × (17 + 11) × 4 ÷ 2 = 112; the top is open, so just the bottom and sides: (11 + 5 + 5) × 36 = 756; 868 in all.

  6. 18. C → B → A

    2 × cross-section + perimeter × length = 168 + 448 = 616 cm².

Numsprite · numsprite.com/en/worksheets/prisms-and-cylinders/surface-area-of-prisms

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