Step-by-step Maths Level 5: Perimeter of rectilinear shapes
Part of the Step-by-step Maths Level 5 perimeter of rectilinear shapes, time and money problems chapter. Chapter overview · whole chapter on one page
Perimeter of rectilinear shapes
A rectilinear shape has only right-angled corners. The perimeter is the distance all the way round, so add every side.
Some sides are not given. Work them out first: a missing side is a longer side take away a shorter part.
Key ideas
- Perimeter = the sum of all the sides.
- Find each missing side by subtraction first.
- A rectangle: 2 × (length + width).
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 10 - 4 = 6 cm; right side = 8 - 3 = 5 cm
- List all six sides. The perimeter is the distance all the way round.4 + 5 + 6 + 3 + 10 + 8 cm
- Add the sides. Add all the lengths together.36 cm
- Write the perimeter. Give the answer with the unit cm.36 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (10 + 8) = 36 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 5 = 4 cm; right side = 7 - 2 = 5 cm
- List all six sides. The perimeter is the distance all the way round.5 + 5 + 4 + 2 + 9 + 7 cm
- Add the sides. Add all the lengths together.32 cm
- Write the perimeter. Give the answer with the unit cm.32 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 7) = 32 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.7 + 4 = 11 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 11 = 22 cm
- Write the perimeter. Give the unit cm.22 cm
Check. Check: 7 + 4 + 7 + 4 = 22 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Watch out
Watch out. Do not leave out a side. An L-shape has six sides, not four.
Exam tip
Grown-up tip. Ask the child to trace the shape with a finger, saying each side aloud, before adding.
Exercise 9A Practice: perimeter
Non-calculatorMethod. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 6 = 3 cm; right side = 7 - 5 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 3 + 5 + 9 + 7 cm
- Add the sides. Add all the lengths together.32 cm
- Write the perimeter. Give the answer with the unit cm.32 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 7) = 32 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 7 - 2 = 5 cm; right side = 5 - 2 = 3 cm
- List all six sides. The perimeter is the distance all the way round.2 + 3 + 5 + 2 + 7 + 5 cm
- Add the sides. Add all the lengths together.24 cm
- Write the perimeter. Give the answer with the unit cm.24 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (7 + 5) = 24 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 6 = 6 cm; right side = 8 - 5 = 3 cm
- List all six sides. The perimeter is the distance all the way round.6 + 3 + 6 + 5 + 12 + 8 cm
- Add the sides. Add all the lengths together.40 cm
- Write the perimeter. Give the answer with the unit cm.40 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 8) = 40 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 10 - 2 = 8 cm; right side = 4 - 2 = 2 cm
- List all six sides. The perimeter is the distance all the way round.2 + 2 + 8 + 2 + 10 + 4 cm
- Add the sides. Add all the lengths together.28 cm
- Write the perimeter. Give the answer with the unit cm.28 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (10 + 4) = 28 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 6 = 3 cm; right side = 6 - 4 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 3 + 4 + 9 + 6 cm
- Add the sides. Add all the lengths together.30 cm
- Write the perimeter. Give the answer with the unit cm.30 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 6) = 30 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.15 + 6 = 21 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 21 = 42 cm
- Write the perimeter. Give the unit cm.42 cm
Check. Check: 15 + 6 + 15 + 6 = 42 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 6 = 6 cm; right side = 7 - 5 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 6 + 5 + 12 + 7 cm
- Add the sides. Add all the lengths together.38 cm
- Write the perimeter. Give the answer with the unit cm.38 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 7) = 38 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 8 = 4 cm; right side = 9 - 6 = 3 cm
- List all six sides. The perimeter is the distance all the way round.8 + 3 + 4 + 6 + 12 + 9 cm
- Add the sides. Add all the lengths together.42 cm
- Write the perimeter. Give the answer with the unit cm.42 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 9) = 42 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.14 + 8 = 22 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 22 = 44 cm
- Write the perimeter. Give the unit cm.44 cm
Check. Check: 14 + 8 + 14 + 8 = 44 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 4 = 5 cm; right side = 8 - 6 = 2 cm
- List all six sides. The perimeter is the distance all the way round.4 + 2 + 5 + 6 + 9 + 8 cm
- Add the sides. Add all the lengths together.34 cm
- Write the perimeter. Give the answer with the unit cm.34 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 8) = 34 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 5 - 2 = 3 cm; right side = 6 - 2 = 4 cm
- List all six sides. The perimeter is the distance all the way round.2 + 4 + 3 + 2 + 5 + 6 cm
- Add the sides. Add all the lengths together.22 cm
- Write the perimeter. Give the answer with the unit cm.22 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (5 + 6) = 22 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.12 + 9 = 21 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 21 = 42 cm
- Write the perimeter. Give the unit cm.42 cm
Check. Check: 12 + 9 + 12 + 9 = 42 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 7 - 5 = 2 cm; right side = 6 - 3 = 3 cm
- List all six sides. The perimeter is the distance all the way round.5 + 3 + 2 + 3 + 7 + 6 cm
- Add the sides. Add all the lengths together.26 cm
- Write the perimeter. Give the answer with the unit cm.26 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (7 + 6) = 26 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.11 + 5 = 16 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 16 = 32 cm
- Write the perimeter. Give the unit cm.32 cm
Check. Check: 11 + 5 + 11 + 5 = 32 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.15 + 9 = 24 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 24 = 48 cm
- Write the perimeter. Give the unit cm.48 cm
Check. Check: 15 + 9 + 15 + 9 = 48 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.13 + 6 = 19 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 19 = 38 cm
- Write the perimeter. Give the unit cm.38 cm
Check. Check: 13 + 6 + 13 + 6 = 38 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.