Year 5: Regular and irregular polygons
Part of the Year 5 angles and shapes chapter. Chapter overview · whole chapter on one page
Regular and irregular polygons
A polygon is a flat shape with straight sides. We name a polygon by its number of sides: a triangle has 3 sides, a quadrilateral 4, a pentagon 5, a hexagon 6 and an octagon 8.
A regular polygon has all its sides equal and all its angles equal. A square is regular. A shape that does not have equal sides and equal angles is irregular.
Key ideas
- Count the sides to name a polygon.
- A regular polygon has all sides equal and all angles equal.
- If one side or one angle is different, the polygon is irregular.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Check the sides and the angles of a square.
- Check the sides. A square has 4 equal sides.4 sides equal
- Check the angles. A square has 4 right angles, and all of them are equal.4 angles of 90°
- Decide. All the sides are equal and all the angles are equal, so it is regular.Yes, a square is regular
Check. A square is regular because both rules are true. ✓
Watch out. Both rules must be true: equal sides AND equal angles.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. A regular shape has equal sides, so multiply the number of sides by the length of one side.
- Count the sides. A regular shape has the same length of side all the way round.5 sides
- Multiply by the length of one side. Every side is the same length, so multiply.5 × 4 = 20
- Write the answer. 20 cm
Check. 20 ÷ 5 = 4. ✓
Watch out. Count the sides carefully. A hexagon has 6 sides, not 5.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Check the lengths of the sides, then decide.
- Write the lengths. A regular hexagon would have 6 sides of the same length.3, 6, 4, 5, 3, 6 cm
- Compare the lengths. The sides are not all the same length.3 ≠ 6 ≠ 4 ≠ 5
- Decide. Because the sides are not equal, the hexagon is irregular.No, it is irregular
Check. Not all the sides are equal, so the rule for regular is broken. ✓
Watch out. One different side is enough to make a shape irregular.
Watch out
A common mistake is to call a shape regular because its sides are equal, forgetting that the angles must be equal too. A rectangle has equal angles but its sides are not all equal, so it is not regular.
Exercise 9F Naming and classifying polygons
Non-calculatorKey words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Count the sides, then use the name for that number of sides.
- Count the sides. Each side is one straight edge.5 sides
- Use the name for that number of sides. A shape with 5 sides is called a pentagon.pentagon
Check. A pentagon has 5 sides. ✓
Watch out. A quadrilateral has 4 sides, a pentagon 5, a hexagon 6 and an octagon 8.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Count the sides, then use the name for that number of sides.
- Count the sides. Each side is one straight edge.6 sides
- Use the name for that number of sides. A shape with 6 sides is called a hexagon.hexagon
Check. A hexagon has 6 sides. ✓
Watch out. A quadrilateral has 4 sides, a pentagon 5, a hexagon 6 and an octagon 8.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Count the sides, then use the name for that number of sides.
- Count the sides. Each side is one straight edge.3 sides
- Use the name for that number of sides. A shape with 3 sides is called a triangle.triangle
Check. A triangle has 3 sides. ✓
Watch out. A quadrilateral has 4 sides, a pentagon 5, a hexagon 6 and an octagon 8.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Count the sides, then use the name for that number of sides.
- Count the sides. Each side is one straight edge.4 sides
- Use the name for that number of sides. A shape with 4 sides is called a quadrilateral.quadrilateral
Check. A quadrilateral has 4 sides. ✓
Watch out. A quadrilateral has 4 sides, a pentagon 5, a hexagon 6 and an octagon 8.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Count the sides, then use the name for that number of sides.
- Count the sides. Each side is one straight edge.8 sides
- Use the name for that number of sides. A shape with 8 sides is called an octagon.octagon
Check. An octagon has 8 sides. ✓
Watch out. A quadrilateral has 4 sides, a pentagon 5, a hexagon 6 and an octagon 8.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. A regular shape has equal sides, so multiply the number of sides by the length of one side.
- Count the sides. A regular shape has the same length of side all the way round.6 sides
- Multiply by the length of one side. Every side is the same length, so multiply.6 × 5 = 30
- Write the answer. 30 cm
Check. 30 ÷ 6 = 5. ✓
Watch out. Count the sides carefully. A hexagon has 6 sides, not 5.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Share the perimeter equally between the sides.
- Divide the perimeter by the length of one side. Every side is 6 cm, so count how many 6 cm sides fit in 36 cm.36 ÷ 6 = 6
- Write the number of sides. A shape with 6 sides is a hexagon.6 sides
Check. 6 × 6 = 36 cm. ✓
Watch out. Divide the perimeter by the length of one side to find the number of sides.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. A regular shape has equal sides, so multiply the number of sides by the length of one side.
- Count the sides. A regular shape has the same length of side all the way round.8 sides
- Multiply by the length of one side. Every side is the same length, so multiply.8 × 7 = 56
- Write the answer. 56 cm
Check. 56 ÷ 8 = 7. ✓
Watch out. Count the sides carefully. A hexagon has 6 sides, not 5.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Look at the lengths of the sides.
- Look at the picture. The sides are different lengths. Some are long and some are short.long and short sides
- Check the rule. A regular shape must have all its sides equal.not all equal
- Decide. So this hexagon is irregular.No
Check. The rule for regular is broken, so the answer is no. ✓
Watch out. One different side makes the shape irregular.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Think about the rules: a regular shape has equal sides and equal angles.
- Look at each shape. A square, a regular pentagon and a regular triangle all have equal sides.square, pentagon, triangle: regular
- Check the rectangle. A rectangle has equal angles, but its sides are not all equal.rectangle: not regular
- Decide. The rectangle is the odd one out, because it is the only shape that is not regular.The rectangle
Check. Only the rectangle has sides that are not all equal. ✓
Watch out. Check the sides as well as the angles.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Think about an example of a regular shape.
- Pick a regular shape. A regular triangle has 3 equal sides and 3 equal angles.regular triangle
- Check its angles. The angles are equal, but they are not right angles.not 90°
- Decide. So Sam is wrong: regular shapes do not have to have right angles.No
Check. A regular triangle has equal sides and angles, but no right angles. ✓
Watch out. A right angle is only in some regular shapes, such as a square.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Share the perimeter equally between the five sides.
- Count the sides. A regular pentagon has 5 equal sides.5 sides
- Divide the perimeter by 5. All the sides are equal, so share the perimeter equally.45 ÷ 5 = 9
- Write the answer. 9 cm
Check. 5 × 9 = 45 cm. ✓
Watch out. The perimeter is the total of all the sides, so divide it to find one side.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Find each perimeter, then take the smaller from the bigger.
- Find the perimeter of the hexagon. A hexagon has 6 sides of 4 cm.6 × 4 = 24 cm
- Find the perimeter of the triangle. A triangle has 3 sides of 4 cm.3 × 4 = 12 cm
- Find the difference. Take the smaller perimeter from the bigger one.24 − 12 = 12 cm
Check. 12 + 12 = 24, the hexagon perimeter. ✓
Watch out. Find each perimeter first. Do not subtract the side lengths.
Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.
Method. Think about what a regular shape needs.
- Write the rule. A regular shape has all its sides equal and all its angles equal.all sides equal
- Compare with the shape. If the sides are not all the same length, the shape cannot be regular.unequal sides
- Write the answer. No
Check. Unequal sides break the rule for a regular shape. ✓
Watch out. Equal sides are needed for a regular shape.