Geometry and proof · Ages 13–14

Regular polygons worksheet

Part of: Polygons

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Geometry and proof · Ages 13–14

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

1.A regular 9-sided polygon turns about its centre. The smallest turn that fits it back onto itself is °.
Answer:
2.The picture shows a regular polygon. It has lines of symmetry.
Answer:
3.A regular 4-sided polygon turns about its centre. The smallest turn that fits it back onto itself is °.
Answer:
4.O is the centre of the regular polygon. x =
Answer:
5.This regular polygon has lines of symmetry and rotational symmetry of order , fitting onto itself every °.
Fill in each blank
Answer:
6.A regular polygon turned 45° about its centre fits onto itself for the first time. It has sides.
Answer:
7.A regular polygon turned 60° about its centre fits onto itself for the first time. It has sides.
Answer:

8.All the sides of a 5-sided polygon are equal. It must be a regular 5-sided polygon.
True or false?
Answer:
9.All the sides of a 3-sided polygon are equal. It must be a regular 3-sided polygon.
True or false?
Answer:
10.All the angles of a 3-sided polygon are equal. It must be a regular 3-sided polygon.
True or false?
Answer:
11.All the angles of a 5-sided polygon are equal. It must be a regular 5-sided polygon.
True or false?
Answer:
12.How many lines of symmetry of a regular 8-sided polygon pass through its vertices?
- A. 16
- B. 4
- C. 6
- D. 8
Choose the right answer
Answer:

13.A sign shaped like a regular 4-sided polygon turns about its centre. The smallest turn that fits it back is °, and it has lines of symmetry.
Fill in each blank
Working:
Answer:
14.A rhombus-shaped tile has four sides of 25 cm, and one of its angles is 70°. Is it a regular polygon?
- A. Yes: opposite angles are equal
- B. Yes: all four sides are equal
- C. No: the sides aren't all equal
- D. No: the sides are equal, but not all the angles are
Choose the right answer
Working:
Answer:
15.A regular polygon's angles at the centre are 72° each. It has 4 lines of symmetry.
True or false?
Working:
Answer:
16.A regular polygon has 20 lines of symmetry. Each of its angles at the centre =
Working:
Answer:
17.A stop sign is a regular octagon with sides of 30 cm. What is its perimeter?
Working:
Answer:
18.A rhombus-shaped tile has four sides of 15 cm, and one of its angles is 80°. Is it a regular polygon?
- A. No: the sides are equal, but not all the angles are
- B. No: the sides aren't all equal
- C. Yes: all four sides are equal
- D. Yes: opposite angles are equal
Choose the right answer
Working:
Answer:

Show the answers and working

Regular polygons worksheet: Answers and working

1. 40
Its 9 equal angles at the centre make a full turn: 360° ÷ 9 = 40°.
2. 6
A regular polygon has as many lines of symmetry as sides: 6 sides, so 6 lines.
3. 90
Its 4 equal angles at the centre make a full turn: 360° ÷ 4 = 90°.
4. 60°
The polygon has 6 sides and 6 equal angles at the centre making a full turn: x = 360° ÷ 6 = 60°.
5. 10, 10, 36
A regular 10-sided polygon: 10 lines of symmetry, order 10, a fit every 360° ÷ 10 = 36°.
6. 8
It fits each time it turns by one angle at the centre, and that angle = 360° ÷ the sides: sides = 360° ÷ 45° = 8.
7. 6
It fits each time it turns by one angle at the centre, and that angle = 360° ÷ the sides: sides = 360° ÷ 60° = 6.

8. False
A triangle with equal sides has three angles of 60°, so it must be regular; with more than 3 sides, the sides can be equal while the angles aren't (a rhombus, say), so it needn't be.
9. True
A triangle with equal sides has three angles of 60°, so it must be regular; with more than 3 sides, the sides can be equal while the angles aren't (a rhombus, say), so it needn't be.
10. True
A triangle with equal angles has equal sides too, so it must be regular; with more than 3 sides, the angles can be equal while the sides aren't (a rectangle, say), so it needn't be.
11. False
A triangle with equal angles has equal sides too, so it must be regular; with more than 3 sides, the angles can be equal while the sides aren't (a rectangle, say), so it needn't be.
12. B. 4
With an even number of sides, half the lines pass through two opposite vertices and half through the middles of opposite sides: 8 ÷ 2 = 4 pass through vertices.

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

13. 90, 4
A regular 4-sided polygon fits every 360° ÷ 4 = 90° and has 4 lines of symmetry.
14. D. No: the sides are equal, but not all the angles are
Neighbouring angles are 70° and 180° − 70° = 110°, not equal, so it isn't regular (a square would be).
15. False
Sides = 360° ÷ 72°, and a regular polygon has as many lines of symmetry as sides.
16. 18°
20 lines of symmetry means 20 sides and 20 equal angles at the centre: 360° ÷ 20 = 18°.
17. 240 cm
A regular octagon's eight sides are equal: perimeter = 8 × 30 = 240 cm.
18. A. No: the sides are equal, but not all the angles are
Neighbouring angles are 80° and 180° − 80° = 100°, not equal, so it isn't regular (a square would be).

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