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Measures and solids · Ages 12–13

Surface area of a prism worksheet

Part of: Prisms

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Surface area of a prism worksheet

Measures and solids · Ages 12–13

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Name:Date:Score:／48

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 cuboid in the picture is 4 cm long, 10 cm wide and 8 cm high. What is its total surface area, in cm²?

    Answer:

  2. 2.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 14 cm long. What is its total surface area, in cm²?

    Answer:

  3. 3.The prism in the picture is 18 cm long, its cross-section a right-angled triangle of sides 8 cm, 6 cm and 10 cm. The two ends make cm², the three sides cm², the total surface area cm².

    Fill in each blank

    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 8 cm long. What is its total surface area, in cm²?

    Answer:

  5. 5.The prism in the picture has a trapezium as its cross-section, 7 cm along the top and 25 cm along the bottom, each slanting side 15 cm; it is 7 cm long. What is the area of all its sides together, in cm²?

    Answer:

  6. 6.The prism in the picture has a trapezium as its cross-section, 5 cm along the top and 11 cm along the bottom, each slanting side 5 cm; it is 5 cm long. What is the area of all its sides together, in cm²?

    Answer:

  7. 7.The prism in the picture has an L-shaped cross-section, 10 cm wide and 12 cm high, both arms 3 cm thick; it is 4 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 480 cm². How long is it?

    Answer:

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

  1. 9.Open out the three sides of the prism in the picture and they join into one rectangle, 12 cm wide. How long is the rectangle?

    • A. 24 cm
    • B. 7 cm
    • C. 6 cm
    • D. 12 cm

    Choose the right answer

    Answer:

  2. 10.Open out the three sides of the prism in the picture and they join into one rectangle, 7 cm wide. How long is the rectangle?

    • A. 84 cm
    • B. 63 cm
    • C. 56 cm
    • D. 31 cm

    Choose the right answer

    Answer:

  3. 11.A prism's cross-section has an area of 21 cm² and a perimeter of 34 cm, and the prism is 19 cm long. Its total surface area is 667 cm².

    True or false?

    Answer:

  4. 12.A prism's cross-section has an area of 33 cm² and a perimeter of 21 cm, and the prism is 18 cm long. Its total surface area is 444 cm².

    True or false?

    Answer:

Part C: Word problems (4 marks each)

  1. 13.A metal trough with no lid is 46 cm long, its cross-section a trapezium: 16 cm across the open top, 4 cm across the bottom, 8 cm deep, each slanting side 10 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:

  2. 14.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 300 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:

  3. 15.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, 16 cm long. Put the steps in order.

    • A. Total = 896 + 2 × 7 × 24 ÷ 2 = 1064
    • B. Sides = 56 × 16 = 896
    • C. Perimeter = 7 + 24 + 25 = 56

    Write the letters in the right order

    Working:

    Answer:

  4. 16.A cuboid gift box is 30 cm long, 16 cm wide and 4 cm high. How many cm² of wrapping paper cover the whole box exactly (no overlaps)?

    Working:

    Answer:

  5. 17.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 20 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:

  6. 18.An open-topped cuboid box is to be made from thin board, its bottom 10 cm by 13 cm and its sides 5 cm high. At least how much board does it take?

    • A. 245 cm²
    • B. 490 cm²
    • C. 375 cm²
    • D. 360 cm²

    Choose the right answer

    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. 304 cm²

    Three pairs of equal faces: 2 × (80 + 40 + 32) = 304 cm².

  2. 2. 384 cm²

    The two ends 2 × (6 × 8 ÷ 2) = 48, the sides = perimeter × length = 24 × 14 = 336; 384 cm² in all.

  3. 3. 48, 432, 480

    Ends 2 × 8 × 6 ÷ 2 = 48; sides (8 + 6 + 10) × 18 = 432; 480 in all.

  4. 4. 600 cm²

    The ends 2 × (18 × 12 ÷ 2) = 216; perimeter 18 + 15 + 15 = 48, sides 48 × 8 = 384; 600 cm² in all.

  5. 5. 434 cm²

    The sides open into one rectangle: the perimeter 7 + 25 + 15 + 15 = 62 cm, times the length 7: 434 cm².

  6. 6. 130 cm²

    The sides open into one rectangle: the perimeter 5 + 11 + 5 + 5 = 26 cm, times the length 5: 130 cm².

  7. 7. 290 cm²

    The cross-section is 57 cm², two of them 114; the L's perimeter is the same as a 10 by 12 rectangle's, 2 × (10 + 12) = 44, so the sides are 44 × 4 = 176; 290 cm² in all.

  8. 8. 18 cm

    The ends are 2 × 6 × 8 ÷ 2 = 48, so the sides are 480 − 48 = 432; the perimeter is 24 cm, so the length = 432 ÷ 24 = 18 cm.

Part B: Choose, or true or false

  1. 9. D. 12 cm

    The three sides laid end to end make the cross-section's perimeter: 4 + 3 + 5 = 12 cm.

  2. 10. C. 56 cm

    The three sides laid end to end make the cross-section's perimeter: 24 + 7 + 25 = 56 cm.

  3. 11. False

    Total surface area = 2 × cross-section + perimeter × length = 2 × 21 + 34 × 19 = 688 cm².

  4. 12. True

    Total surface area = 2 × cross-section + perimeter × length = 2 × 33 + 21 × 18 = 444 cm².

Part C: Word problems

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

  1. 13. 160, 1104, 1264

    The ends: 2 × (16 + 4) × 8 ÷ 2 = 160; the top is open, so just the bottom and sides: (4 + 10 + 10) × 46 = 1104; 1264 in all.

  2. 14. 158400 cm²

    Ends 2 × (240 × 160 ÷ 2) = 38400; the two slopes 2 × 200 × 300 = 120000; no floor, so the bottom isn't counted: 158400 cm².

  3. 15. C → B → A

    2 × cross-section + perimeter × length = 168 + 896 = 1064 cm².

  4. 16. 1328 cm²

    Six faces, three pairs: 2 × (30 × 16 + 16 × 4 + 30 × 4) = 1328 cm².

  5. 17. 5.76 dollars

    Total surface area 2 × 12 × 16 ÷ 2 + (12 + 16 + 20) × 20 = 1152 cm², and 1152 ÷ 100 × 0.5 = $5.76.

  6. 18. D. 360 cm²

    One bottom, 10 × 13, and four sides, 2 × 13 × 5 + 2 × 10 × 5: 360 cm².

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