Shape and space · Ages 10–11
Surface area worksheet
Part of: Solid shapes
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Surface area worksheet
Shape and space · Ages 10–11
Numsprite
numsprite.com
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.A cube's edges are 19 cm long. What is its surface area, in cm²?
Answer:
2.A cuboid is 4 cm long, 13 cm wide and 6 cm high. What is its surface area, in cm²?
Answer:
3.A cuboid is 5 cm long, 6 cm wide and 9 cm high. What is its surface area, in cm²?
Answer:
4.A cube's edges are 3 cm long. What is its surface area, in cm²?
Answer:
5.A square pyramid's base is a square with 3 cm sides, and its four side faces are triangles with base 3 cm and height 4 cm. What is its surface area, in cm²?
Answer:
6.A cube's surface area is 150 cm². How long is each edge, in cm?
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7.A square pyramid's base is a square with 3 cm sides, and its four side faces are triangles with base 3 cm and height 9 cm. What is its surface area, in cm²?
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8.A cube's surface area is 294 cm². How long is each edge, in cm?
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9.A triangular prism is 16 cm long. Its two ends are right-angled triangles with sides 9 cm, 12 cm and 15 cm (the 9 cm and 12 cm sides are at right angles). What is its surface area, in cm²?
Answer:
10.A triangular prism is 8 cm long. Its two ends are right-angled triangles with sides 3 cm, 4 cm and 5 cm (the 3 cm and 4 cm sides are at right angles). What is its surface area, in cm²?
Answer:
Part B: Choose, or true or false (2 marks each)
11.A cuboid is 14 cm long, 7 cm wide and 4 cm high. Which calculation gives its surface area?
- A. 14 × 7 + 14 × 4 + 7 × 4
- B. 4 × (14 + 7 + 4)
- C. 2 × (14 × 7 + 14 × 4 + 7 × 4)
- D. 14 × 7 × 4
Choose the right answer
Answer:
12.A cuboid is 5 cm long, 14 cm wide and 3 cm high. Which calculation gives its surface area?
- A. 5 × 14 + 5 × 3 + 14 × 3
- B. 5 × 14 × 3
- C. 4 × (5 + 14 + 3)
- D. 2 × (5 × 14 + 5 × 3 + 14 × 3)
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A cuboid box 21 cm by 16 cm by 17 cm is opened out flat into its net (no glue flaps). What is the net's area, in cm²?
Working:
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14.Ming's bedroom is 6 m long, 5 m wide and 2 m high. All four walls get wallpaper, but not the floor or the ceiling (ignore the door and windows). How many square metres of wallpaper are needed?
Working:
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15.A tent is a triangular prism. Its front and back are triangles with base 12 m and height 8 m; each of its two sloping sides is a sheet 2 m long and 10 m wide; there is no floor. How many square metres of canvas does the tent need?
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16.Ka-yee makes a cuboid box with no lid from card, 14 cm long, 8 cm wide and 15 cm high. At least how many cm² of card are needed?
Working:
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17.Tsz-ching wraps a gift box shaped like a square pyramid exactly in paper. Its base is a square with 8 cm sides, and its four side faces are triangles with base 8 cm and height 13 cm. At least how many cm² of paper are needed?
Working:
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18.Ming makes a cuboid box with no lid from card, 7 cm long, 4 cm wide and 18 cm high. At least how many cm² of card are needed?
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Answer:
Show the answers and working
Surface area worksheet: Answers and working
Part A: Working out and filling in
1. 2166 cm²
A cube has six equal square faces. Work out one face first: 19 × 19.
6 equal squares: each 19 × 19 = 361, and 6 × 361 = 2166.
2. 308 cm²
Opposite faces of a cuboid match. Work out the three different faces first: 4 × 13, 4 × 6 and 13 × 6.
The three different faces: 52, 24 and 78, adding to 154; there are 2 of each: 154 × 2 = 308.
3. 258 cm²
Opposite faces of a cuboid match. Work out the three different faces first: 5 × 6, 5 × 9 and 6 × 9.
The three different faces: 30, 45 and 54, adding to 129; there are 2 of each: 129 × 2 = 258.
4. 54 cm²
A cube has six equal square faces. Work out one face first: 3 × 3.
6 equal squares: each 3 × 3 = 9, and 6 × 9 = 54.
5. 33 cm²
Surface area = the square base + four triangles. Work out the base, 3 × 3, then one triangle's area.
Base: 3 × 3 = 9; four triangles: 4 × 3 × 4 ÷ 2 = 24; in all 9 + 24 = 33.
6. 5 cm
A cube's six faces are equal. Find one face's area from 150, then think which number times itself gives it.
Each face is 150 ÷ 6 = 25; 5 × 5 = 25, so each edge is 5.
7. 63 cm²
Surface area = the square base + four triangles. Work out the base, 3 × 3, then one triangle's area.
Base: 3 × 3 = 9; four triangles: 4 × 3 × 9 ÷ 2 = 54; in all 9 + 54 = 63.
8. 7 cm
A cube's six faces are equal. Find one face's area from 294, then think which number times itself gives it.
Each face is 294 ÷ 6 = 49; 7 × 7 = 49, so each edge is 7.
9. 684 cm²
A triangular prism has two triangles and three rectangles. Start with one right-angled triangle: its perpendicular sides are 9 and 12.
All three rectangles are 16 cm long; their widths are the triangle's three sides.
Two triangles: 2 × 9 × 12 ÷ 2 = 108; three rectangles: (9 + 12 + 15) × 16 = 576; in all 684.
10. 108 cm²
A triangular prism has two triangles and three rectangles. Start with one right-angled triangle: its perpendicular sides are 3 and 4.
All three rectangles are 8 cm long; their widths are the triangle's three sides.
Two triangles: 2 × 3 × 4 ÷ 2 = 12; three rectangles: (3 + 4 + 5) × 8 = 96; in all 108.
Part B: Choose, or true or false
11. C. 2 × (14 × 7 + 14 × 4 + 7 × 4)
Surface area adds up all six faces. Which three faces come in pairs? See which calculation counts every one of them.
A cuboid has 3 pairs of matching faces: 2 × (14 × 7 + 14 × 4 + 7 × 4) = 364.
12. D. 2 × (5 × 14 + 5 × 3 + 14 × 3)
Surface area adds up all six faces. Which three faces come in pairs? See which calculation counts every one of them.
A cuboid has 3 pairs of matching faces: 2 × (5 × 14 + 5 × 3 + 14 × 3) = 254.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 1930 cm²
The net's area is the box's six faces. Work out the three different faces first: 21 × 16, 21 × 17 and 16 × 17.
6 faces in matching pairs: 2 × (21 × 16 + 21 × 17 + 16 × 17) = 1930.
14. 44 m²
Only the four walls count. Two walls are 6 × 2; what are the other two? Or open all four walls out into one long rectangle.
Only the four walls: opened out they make one rectangle, as long as the way round the room, 2 × (6 + 5) = 22, and 2 high: 22 × 2 = 44.
15. 136 m²
The canvas covers two triangles and two sloping sheets, not the floor. Start with one triangle: 12 × 8 ÷ 2.
Two triangles: 2 × 12 × 8 ÷ 2 = 96; two sloping sheets: 2 × 2 × 10 = 40; in all 136.
16. 772 cm²
With no lid, only five faces count: the base and four sides. Start with the base, 14 × 8.
No lid, so 5 faces: the base 14 × 8 = 112, the four sides 2 × (14 × 15 + 8 × 15) = 660; in all 772.
17. 272 cm²
The paper is the box's surface area: the square base plus four triangles. Start with the base, 8 × 8.
The paper is the surface area: 8 × 8 + 4 × 8 × 13 ÷ 2 = 64 + 208 = 272.
18. 424 cm²
With no lid, only five faces count: the base and four sides. Start with the base, 7 × 4.
No lid, so 5 faces: the base 7 × 4 = 28, the four sides 2 × (7 × 18 + 4 × 18) = 396; in all 424.
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