Year 4: Perimeter
Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Perimeter
The perimeter of a shape is the distance all the way round its edge. Imagine walking round the edge of a field and ending up where you started. The length of your walk is the perimeter. We measure it in cm or m (the same units as length).
Rectangles. A rectangle has 2 long sides and 2 short sides. Opposite sides are equal. So we only need to know two sides. Add all four sides, or add the length and the width and double it.
Squares. A square has 4 equal sides. For a square with sides of 6 m, the perimeter is 6 + 6 + 6 + 6 = 4 × 6 = 24 m.
Shapes with missing sides. Some sides are not labelled. We can work them out. Imagine walking all the way round and back to the start. You go right exactly as far as you go left. And you go down exactly as far as you go up. In this shape, the top is 8 cm. The sides along the bottom must also add up to 8 cm. One of them is 4 cm, so side a = 8 − 4 = 4 cm.
Key words. The perimeter is the distance round a shape. A rectilinear shape has straight sides that meet at right angles. A square has 4 equal sides. A rectangle has 2 pairs of equal sides.
Key ideas
- Perimeter = the distance all the way round the edge. Units: cm or m.
- Rectangle: add all four sides, or double (length + width).
- Square: 4 × the side.
- Missing sides: you go right as far as you go left, and down as far as you go up.
- Add ALL the sides, including the ones you worked out.
- Perimeter is a length, so it is in cm or m (not cm²).
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 4
Right: 4
Bottom: 4
Left: 4 - Add them. 4 + 4 = 8
8 + 4 = 12
12 + 4 = 16 - Write the perimeter with its unit. Perimeter = 16 cm
Check. The top (4) matches the bottom (4), and the left (4) matches the right (4). That is a good sign. 2 × (4 + 4) = 16. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.9 cm, 4 cm, 9 cm, 4 cm
- Add the sides, one at a time. The perimeter is all the sides added together.9 + 4 = 13
13 + 9 = 22
22 + 4 = 26 - Write the perimeter with its unit. Perimeter = 26 cm
Check. Another way: double the length and the width. 2 × (9 + 4) = 2 × 13 = 26. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has four equal sides, so the perimeter is 4 times the side length.
- Remember: a square has 4 equal sides. We only need one side length.Each side is 6 m.
- Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.6 + 6 + 6 + 6 = 4 × 6 = 24 m
- Write the perimeter with its unit. Perimeter = 24 m
Check. Half way: 6 + 6 = 12 and 12 + 12 = 24. ✓
Watch out. Do not just give one side. The perimeter goes all the way round.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Add the length and the width. These two sides are half of the way round.20 + 8 = 28 m
- Double it. The other two sides are the same, so we go round twice.2 × 28 = 56 m
- Write the perimeter with its unit. Perimeter = 56 m
Check. Add all four sides: 20 + 8 + 20 + 8 = 56. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.8 cm, 3 cm, 4 cm, 3 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 8
Going left: 4 + a
These are equal, so: a = 8 − 4 = 4 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 3 + 3
Going up: b
These are equal, so: b = 6 cm - Add all the sides. Now every side has a length. Add them one at a time.8 + 3 = 11
11 + 4 = 15
15 + 3 = 18
18 + 4 = 22
22 + 6 = 28 - Write the perimeter with its unit. Perimeter = 28 cm
Check. The shape fits inside a 8 cm by 6 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (8 + 6) = 28. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.10 cm, 4 cm, 4 cm, 3 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 10
Going left: 4 + a
These are equal, so: a = 10 − 4 = 6 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 4 + 3
Going up: b
These are equal, so: b = 7 cm - Add all the sides. Now every side has a length. Add them one at a time.10 + 4 = 14
14 + 4 = 18
18 + 3 = 21
21 + 6 = 27
27 + 7 = 34 - Write the perimeter with its unit. Perimeter = 34 cm
Check. The shape fits inside a 10 cm by 7 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (10 + 7) = 34. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.9 cm, 2 cm, 3 cm, 3 cm, 3 cm, 3 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 9
Going left: 3 + 3 + a
These are equal, so: a = 9 − 6 = 3 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 2 + 3
Going up: 3 + b
These are equal, so: b = 5 − 3 = 2 cm - Add all the sides. Now every side has a length. Add them one at a time.9 + 2 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
20 + 3 = 23
23 + 3 = 26
26 + 2 = 28 - Write the perimeter with its unit. Perimeter = 28 cm
Check. The shape fits inside a 9 cm by 5 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (9 + 5) = 28. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.
- Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.2 × 12 = 24 cm
38 − 24 = 14 cm - Share what is left between the two other sides. The two other sides are equal, so halve the answer.14 ÷ 2 = 7 cm
- Write the answer. The other side is 7 cm.
Check. Check by adding: 12 + 7 + 12 + 7 = 38. ✓
Watch out. Do not halve the perimeter and stop. Take away the known sides first.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has 4 equal sides, so divide the perimeter by 4.
- Remember: the 4 sides of a square are equal. So the perimeter is 4 times one side.4 × side = 36 cm
- Divide the perimeter by 4. Division is the opposite of multiplying.36 ÷ 4 = 9 cm
- Write the answer. Each side is 9 cm.
Check. 4 × 9 = 36. ✓
Watch out. Divide by 4, not by 2.
Watch out
Do not forget the sides you cannot see numbers on. Count all the sides (an L-shape has 6). Do not multiply the length by the width: that gives the area, not the perimeter. And for a rectangle you need four sides, not two.Exercise 7H Perimeter
Non-calculatorKey words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 5
Right: 3
Bottom: 5
Left: 3 - Add them. 5 + 3 = 8
8 + 5 = 13
13 + 3 = 16 - Write the perimeter with its unit. Perimeter = 16 cm
Check. The top (5) matches the bottom (5), and the left (3) matches the right (3). That is a good sign. 2 × (5 + 3) = 16. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 5
Right: 3
Bottom: 5
Left: 3 - Add them. 5 + 3 = 8
8 + 5 = 13
13 + 3 = 16 - Write the perimeter with its unit. Perimeter = 16 cm
Check. The top (5) matches the bottom (5), and the left (3) matches the right (3). That is a good sign. 2 × (5 + 3) = 16. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 3
Right: 3
Bottom: 3
Left: 3 - Add them. 3 + 3 = 6
6 + 3 = 9
9 + 3 = 12 - Write the perimeter with its unit. Perimeter = 12 cm
Check. The top (3) matches the bottom (3), and the left (3) matches the right (3). That is a good sign. 2 × (3 + 3) = 12. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.7 cm, 3 cm, 7 cm, 3 cm
- Add the sides, one at a time. The perimeter is all the sides added together.7 + 3 = 10
10 + 7 = 17
17 + 3 = 20 - Write the perimeter with its unit. Perimeter = 20 cm
Check. Another way: double the length and the width. 2 × (7 + 3) = 2 × 10 = 20. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.10 cm, 6 cm, 10 cm, 6 cm
- Add the sides, one at a time. The perimeter is all the sides added together.10 + 6 = 16
16 + 10 = 26
26 + 6 = 32 - Write the perimeter with its unit. Perimeter = 32 cm
Check. Another way: double the length and the width. 2 × (10 + 6) = 2 × 16 = 32. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.12 m, 5 m, 12 m, 5 m
- Add the sides, one at a time. The perimeter is all the sides added together.12 + 5 = 17
17 + 12 = 29
29 + 5 = 34 - Write the perimeter with its unit. Perimeter = 34 m
Check. Another way: double the length and the width. 2 × (12 + 5) = 2 × 17 = 34. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.15 m, 8 m, 15 m, 8 m
- Add the sides, one at a time. The perimeter is all the sides added together.15 + 8 = 23
23 + 15 = 38
38 + 8 = 46 - Write the perimeter with its unit. Perimeter = 46 m
Check. Another way: double the length and the width. 2 × (15 + 8) = 2 × 23 = 46. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has four equal sides, so the perimeter is 4 times the side length.
- Remember: a square has 4 equal sides. We only need one side length.Each side is 8 cm.
- Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.8 + 8 + 8 + 8 = 4 × 8 = 32 cm
- Write the perimeter with its unit. Perimeter = 32 cm
Check. Half way: 8 + 8 = 16 and 16 + 16 = 32. ✓
Watch out. Do not just give one side. The perimeter goes all the way round.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has four equal sides, so the perimeter is 4 times the side length.
- Remember: a square has 4 equal sides. We only need one side length.Each side is 15 m.
- Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.15 + 15 + 15 + 15 = 4 × 15 = 60 m
- Write the perimeter with its unit. Perimeter = 60 m
Check. Half way: 15 + 15 = 30 and 30 + 30 = 60. ✓
Watch out. Do not just give one side. The perimeter goes all the way round.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has four equal sides, so the perimeter is 4 times the side length.
- Remember: a square has 4 equal sides. We only need one side length.Each side is 25 cm.
- Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.25 + 25 + 25 + 25 = 4 × 25 = 100 cm
- Write the perimeter with its unit. Perimeter = 100 cm
Check. Half way: 25 + 25 = 50 and 50 + 50 = 100. ✓
Watch out. Do not just give one side. The perimeter goes all the way round.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.6 cm, 2 cm, 3 cm, 3 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 6
Going left: 3 + a
These are equal, so: a = 6 − 3 = 3 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 2 + 3
Going up: b
These are equal, so: b = 5 cm - Add all the sides. Now every side has a length. Add them one at a time.6 + 2 = 8
8 + 3 = 11
11 + 3 = 14
14 + 3 = 17
17 + 5 = 22 - Write the perimeter with its unit. Perimeter = 22 cm
Check. The shape fits inside a 6 cm by 5 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (6 + 5) = 22. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.5 cm, 4 cm, 3 cm, 2 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 5
Going left: 3 + a
These are equal, so: a = 5 − 3 = 2 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 4 + 2
Going up: b
These are equal, so: b = 6 cm - Add all the sides. Now every side has a length. Add them one at a time.5 + 4 = 9
9 + 3 = 12
12 + 2 = 14
14 + 2 = 16
16 + 6 = 22 - Write the perimeter with its unit. Perimeter = 22 cm
Check. The shape fits inside a 5 cm by 6 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (5 + 6) = 22. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.9 cm, 2 cm, 3 cm, 3 cm, 3 cm, 3 cm, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 9
Going left: 3 + 3 + a
These are equal, so: a = 9 − 6 = 3 cm - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 2 + 3
Going up: 3 + b
These are equal, so: b = 5 − 3 = 2 cm - Add all the sides. Now every side has a length. Add them one at a time.9 + 2 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
20 + 3 = 23
23 + 3 = 26
26 + 2 = 28 - Write the perimeter with its unit. Perimeter = 28 cm
Check. The shape fits inside a 9 cm by 5 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (9 + 5) = 28. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.
- Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.2 × 9 = 18 cm
30 − 18 = 12 cm - Share what is left between the two other sides. The two other sides are equal, so halve the answer.12 ÷ 2 = 6 cm
- Write the answer. The other side is 6 cm.
Check. Check by adding: 9 + 6 + 9 + 6 = 30. ✓
Watch out. Do not halve the perimeter and stop. Take away the known sides first.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.
- Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.2 × 14 = 28 cm
46 − 28 = 18 cm - Share what is left between the two other sides. The two other sides are equal, so halve the answer.18 ÷ 2 = 9 cm
- Write the answer. The other side is 9 cm.
Check. Check by adding: 14 + 9 + 14 + 9 = 46. ✓
Watch out. Do not halve the perimeter and stop. Take away the known sides first.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.
- Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.2 × 20 = 40 cm
52 − 40 = 12 cm - Share what is left between the two other sides. The two other sides are equal, so halve the answer.12 ÷ 2 = 6 cm
- Write the answer. The other side is 6 cm.
Check. Check by adding: 20 + 6 + 20 + 6 = 52. ✓
Watch out. Do not halve the perimeter and stop. Take away the known sides first.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has 4 equal sides, so divide the perimeter by 4.
- Remember: the 4 sides of a square are equal. So the perimeter is 4 times one side.4 × side = 28 cm
- Divide the perimeter by 4. Division is the opposite of multiplying.28 ÷ 4 = 7 cm
- Write the answer. Each side is 7 cm.
Check. 4 × 7 = 28. ✓
Watch out. Divide by 4, not by 2.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. A square has 4 equal sides, so divide the perimeter by 4.
- Remember: the 4 sides of a square are equal. So the perimeter is 4 times one side.4 × side = 60 m
- Divide the perimeter by 4. Division is the opposite of multiplying.60 ÷ 4 = 15 m
- Write the answer. Each side is 15 m.
Check. 4 × 15 = 60. ✓
Watch out. Divide by 4, not by 2.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.
- Write down all four sides. A garden has two long sides and two short sides. Opposite sides are equal.14 m, 9 m, 14 m, 9 m
- Add the sides, one at a time. The perimeter is all the sides added together.14 + 9 = 23
23 + 14 = 37
37 + 9 = 46 - Write the perimeter with its unit. Perimeter = 46 m
Check. Another way: double the length and the width. 2 × (14 + 9) = 2 × 23 = 46. ✓
Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the distance round the playground once. Then double it for two laps.
- Find the perimeter. One lap is the perimeter of the playground. The sides are 30 m and 20 m.30 + 20 + 30 + 20 = 100 m
- Multiply by the number of laps. Mia runs round twice.2 × 100 = 200 m
Check. One lap is 100 m. Two laps is 100 + 100 = 200 m. ✓
Watch out. One lap is one perimeter. Remember to do it twice.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.
- Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.7 m, 3 m, 3 m, 3 m, a, b
- Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.Going right: 7
Going left: 3 + a
These are equal, so: a = 7 − 3 = 4 m - Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.Going down: 3 + 3
Going up: b
These are equal, so: b = 6 m - Add all the sides. Now every side has a length. Add them one at a time.7 + 3 = 10
10 + 3 = 13
13 + 3 = 16
16 + 4 = 20
20 + 6 = 26 - Write the perimeter with its unit. Perimeter = 26 m
Check. The shape fits inside a 7 m by 6 m rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (7 + 6) = 26. ✓
Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 6
Right: 2
Bottom: 6
Left: 2 - Add them. 6 + 2 = 8
8 + 6 = 14
14 + 2 = 16 - Write the perimeter with its unit. Perimeter = 16 cm
Check. The top (6) matches the bottom (6), and the left (2) matches the right (2). That is a good sign. 2 × (6 + 2) = 16. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 4
Right: 4
Bottom: 4
Left: 4 - Add them. 4 + 4 = 8
8 + 4 = 12
12 + 4 = 16 - Write the perimeter with its unit. Perimeter = 16 cm
Check. The top (4) matches the bottom (4), and the left (4) matches the right (4). That is a good sign. 2 × (4 + 4) = 16. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Compare the two perimeters. They are the same size.
- Look at the perimeters. We found the perimeter of each shape in parts (a) and (b).Shape A = 16 cm. Shape B = 16 cm.
- Compare. Equal perimeters mean the distance round the edge is the same.16 cm = 16 cm, so the perimeters are equal.
Check. Shape A: 2 × (6 + 2) = 16. Shape B: 4 × 4 = 16. ✓
Watch out. Shapes that look different can have the same perimeter.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Work out the perimeter correctly, and see what Zainab did.
- Look at what Zainab did. Zainab multiplied the length by the width.8 × 3 = 24
- Find the mistake. 8 × 3 is the number of squares inside the rectangle (the area). The perimeter is the distance round the edge.She found the area, not the perimeter.
- Work out the correct perimeter. Add all four sides: 8, 3, 8 and 3.8 + 3 + 8 + 3 = 22 cm
Check. 2 × (8 + 3) = 2 × 11 = 22. ✓
Watch out. Perimeter: add the sides. Area: multiply.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is 14 cm, so the length and width add up to half of that. Find every pair of whole numbers that add up to 7.
- Find half of the perimeter. A rectangle has two lengths and two widths, so length + width is half of the perimeter.14 ÷ 2 = 7 cm
- List the pairs of numbers that make 7. The length is the longer side. List them from the biggest length.6 + 1 = 7 5 + 2 = 7 4 + 3 = 7
- Check each rectangle. 3 cm by 4 cm: 3 + 4 + 3 + 4 = 14 cm
2 cm by 5 cm: 2 + 5 + 2 + 5 = 14 cm
1 cm by 6 cm: 1 + 6 + 1 + 6 = 14 cm
Check. There are no other pairs: 7 + 0 does not make a rectangle. ✓
Watch out. A rectangle 6 cm by 1 cm is the same rectangle as 1 cm by 6 cm turned round.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. Think about how the perimeter of a rectangle is made. Half of the perimeter is length + width.
- Half of 15 cm. Length + width is half of the perimeter.15 ÷ 2 = 7.5 cm
- Look at the whole-number sides. Two whole numbers added together always make a whole number.length + width must be a whole number, but 7.5 is not
- Decide. Also the perimeter of a rectangle is made of 2 lengths and 2 widths, which is always an even number.No. The perimeter must be an even number.
Check. 15 is odd, so 15 cannot be 2 × (a whole number). ✓
Watch out. Check by trying: 2 × (3 + 4) = 14 and 2 × (4 + 4) = 16, so 15 is skipped.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The square tells us the perimeter. Then take away the two known sides and halve what is left.
- Find the perimeter of the square. A square has 4 equal sides of 9 cm.4 × 9 = 36 cm
- Take away the two 12 cm sides of the rectangle. The rectangle has the same perimeter as the square.2 × 12 = 24 and 36 − 24 = 12 cm
- Halve to find one width. There are two equal widths.12 ÷ 2 = 6 cm
Check. 12 + 6 + 12 + 6 = 36. ✓
Watch out. Do not forget to halve at the end.