Shape and space · Ages 9–10

Regular polygons and tiling worksheet

Part of: Quadrilaterals, tiling and the eight directions

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Shape and space · Ages 9–10

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

1.A regular polygon with 7 sides has sides 3 cm long. What is its perimeter in cm?
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2.A regular polygon with 7 sides has sides 6 cm long. What is its perimeter in cm?
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3.A regular polygon with 5 sides has sides 15 cm long. What is its perimeter in cm?
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4.A regular polygon with 7 sides has a perimeter of 21 cm. How long is each side in cm?
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5.Some identical tiles meet at a point, each with an angle of 40° there. How many are needed to make exactly 360°, with no gap?
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6.A regular polygon with 6 sides has a perimeter of 84 cm. How long is each side in cm?
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7.Some identical tiles meet at a point, each with an angle of 45° there. How many are needed to make exactly 360°, with no gap?
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8.Some identical tiles meet at a point, each with an angle of 90° there. How many are needed to make exactly 360°, with no gap?
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9.A regular polygon with 5 sides has a perimeter of 20 cm. How long is each side in cm?
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13.Square floor tiles 50 cm along each side exactly cover a rectangular floor 200 cm long and 500 cm wide, with no gaps or overlaps. How many tiles are needed?
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14.Square tiles cover a square platform exactly, 5 along each side. How many tiles are in the outermost ring?
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15.A flower bed's fence is a regular polygon with 5 sides, each 5 m long. Fencing costs $39 a metre. How much does the whole fence cost?
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16.Ka-yee bends a wire into a regular polygon with 9 sides, each 12 cm long, then straightens it and bends it into a square. How long is each side of the square in cm?
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17.Ka-lok bends a wire into a regular polygon with 9 sides, each 12 cm long, then straightens it and bends it into a square. How long is each side of the square in cm?
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18.Square floor tiles 40 cm along each side exactly cover a rectangular floor 440 cm long and 240 cm wide, with no gaps or overlaps. How many tiles are needed?
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Show the answers and working

Regular polygons and tiling worksheet: Answers and working

1. 21 cm
It has 7 sides, each 3 cm. The perimeter is all the sides added up.
A regular polygon's 7 sides are all the same length: 7 × 3 = 21.
2. 42 cm
It has 7 sides, each 6 cm. The perimeter is all the sides added up.
A regular polygon's 7 sides are all the same length: 7 × 6 = 42.
3. 75 cm
It has 5 sides, each 15 cm. The perimeter is all the sides added up.
A regular polygon's 5 sides are all the same length: 5 × 15 = 75.
4. 3 cm
All 7 sides are equal, so share the 21 cm perimeter equally among them.
The 7 sides are equal: 21 ÷ 7 = 3.
5. 9 tiles
Each tile gives 40°, and you need 360°. How many lots of 40 make 360?
Each tile gives 40° at the point, and a full turn is 360°: 360 ÷ 40 = 9 tiles. Check: 9 × 40° = 360°.
6. 14 cm
All 6 sides are equal, so share the 84 cm perimeter equally among them.
The 6 sides are equal: 84 ÷ 6 = 14.
7. 8 tiles
Each tile gives 45°, and you need 360°. How many lots of 45 make 360?
Each tile gives 45° at the point, and a full turn is 360°: 360 ÷ 45 = 8 tiles. Check: 8 × 45° = 360°.
8. 4 tiles
Each tile gives 90°, and you need 360°. How many lots of 90 make 360?
Each tile gives 90° at the point, and a full turn is 360°: 360 ÷ 90 = 4 tiles. Check: 4 × 90° = 360°.
9. 4 cm
All 5 sides are equal, so share the 20 cm perimeter equally among them.
The 5 sides are equal: 20 ÷ 5 = 4.

10. C
Read the labels on each shape: are all the sides equal? Are all the angles equal?
A regular polygon has every side equal and every angle equal: it must have both.
11. False
Compare the side lengths one by one, then compare the angles.
Read the side lengths and angles marked: a regular polygon needs all its sides equal and all its angles equal.
12. B. A regular polygon with 9 sides
To tile, the angles meeting at a point must make exactly 360°. Think about the size of each option's angle.
The angles of a regular polygon with 9 sides can't meet at a point to make exactly 360°: there is always a gap or an overlap.

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

13. 40 tiles
First work out how many tiles fit along the length, 200 ÷ 50; then do the same for the width.
200 ÷ 50 = 4 tiles along the length and 500 ÷ 50 = 10 along the width: 4 × 10 = 40 tiles.
14. 16 tiles
Count 5 tiles along each of the four sides, then ask whether the corner tiles got counted twice.
Four sides of 5 each, but the four corner tiles are counted twice: 4 × 5 − 4 = 16.
15. 975 dollars
First find the fence's length: 5 sides of 5 m each.
Then price it at $39 a metre.
The fence is 5 × 5 = 25 m long, and 25 × 39 = 975 dollars.
16. 27 cm
The wire's length doesn't change. First work out how much wire the 9-sided shape uses.
The square uses the same wire, and it has 4 equal sides.
The wire is 9 × 12 = 108 cm; a square's 4 sides are equal: 108 ÷ 4 = 27.
17. 27 cm
The wire's length doesn't change. First work out how much wire the 9-sided shape uses.
The square uses the same wire, and it has 4 equal sides.
The wire is 9 × 12 = 108 cm; a square's 4 sides are equal: 108 ÷ 4 = 27.
18. 66 tiles
First work out how many tiles fit along the length, 440 ÷ 40; then do the same for the width.
440 ÷ 40 = 11 tiles along the length and 240 ÷ 40 = 6 along the width: 11 × 6 = 66 tiles.

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