Year 6 Arithmetic (SATs): Perimeter of composite rectilinear shapes
Part of the Year 6 Arithmetic (SATs) measures and conversions chapter. Chapter overview · whole chapter on one page
Perimeter of composite rectilinear shapes
Rule
A composite shape is made of rectangles. Its perimeter is the total length of all its outside edges.
For an L-shape, the missing sides are found by subtracting. Check the total: an L-shape cut from a rectangle has the same perimeter as the rectangle around it.
Key ideas
- The perimeter is the distance all the way around the outside.
- Find any missing lengths by subtracting from a known length.
- An L-shape has the same perimeter as the rectangle around it.
Method. Find each missing side, then add all six sides.
- Find the missing lengths. The notch is 4 cm by 3 cm, so the sides are 5 cm, 6 cm and so on.8 - 3 = 5, 10 - 4 = 6
- List the six sides. An L-shape has six straight sides.10 cm, 5 cm, 4 cm, 3 cm, 6 cm, 8 cm
- Add the sides. Add every side to get the perimeter.10 + 5 + 4 + 3 + 6 + 8 = 36
- Write the answer. 36 cm
Check. 2 × (10 + 8) = 36 cm. ✓
Watch out. Do not forget the missing sides; there are six sides, not four.
Method. Use the same method: find the missing sides, then add.
- Find the missing lengths. The notch is 5 cm by 4 cm, so the sides are 5 cm, 7 cm and so on.9 - 4 = 5, 12 - 5 = 7
- List the six sides. An L-shape has six straight sides.12 cm, 5 cm, 5 cm, 4 cm, 7 cm, 9 cm
- Add the sides. Add every side to get the perimeter.12 + 5 + 5 + 4 + 7 + 9 = 42
- Write the answer. 42 m
Check. 2 × (12 + 9) = 42 m. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 2 cm by 2 cm, so the sides are 3 cm, 7 cm and so on.5 - 2 = 3, 9 - 2 = 7
- List the six sides. An L-shape has six straight sides.9 cm, 3 cm, 2 cm, 2 cm, 7 cm, 5 cm
- Add the sides. Add every side to get the perimeter.9 + 3 + 2 + 2 + 7 + 5 = 28
- Write the answer. 28 m
Check. 2 × (9 + 5) = 28 m. ✓
Exercise 8D Practice: perimeter of composite shapes
Non-calculatorMethod. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 5 cm by 4 cm, so the sides are 5 cm, 7 cm and so on.9 - 4 = 5, 12 - 5 = 7
- List the six sides. An L-shape has six straight sides.12 cm, 5 cm, 5 cm, 4 cm, 7 cm, 9 cm
- Add the sides. Add every side to get the perimeter.12 + 5 + 5 + 4 + 7 + 9 = 42
- Write the answer. 42 cm
Check. 2 × (12 + 9) = 42 cm. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 6 cm by 5 cm, so the sides are 5 cm, 8 cm and so on.10 - 5 = 5, 14 - 6 = 8
- List the six sides. An L-shape has six straight sides.14 cm, 5 cm, 6 cm, 5 cm, 8 cm, 10 cm
- Add the sides. Add every side to get the perimeter.14 + 5 + 6 + 5 + 8 + 10 = 48
- Write the answer. 48 cm
Check. 2 × (14 + 10) = 48 cm. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 3 cm by 2 cm, so the sides are 5 cm, 6 cm and so on.7 - 2 = 5, 9 - 3 = 6
- List the six sides. An L-shape has six straight sides.9 cm, 5 cm, 3 cm, 2 cm, 6 cm, 7 cm
- Add the sides. Add every side to get the perimeter.9 + 5 + 3 + 2 + 6 + 7 = 32
- Write the answer. 32 cm
Check. 2 × (9 + 7) = 32 cm. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 7 cm by 6 cm, so the sides are 5 cm, 8 cm and so on.11 - 6 = 5, 15 - 7 = 8
- List the six sides. An L-shape has six straight sides.15 cm, 5 cm, 7 cm, 6 cm, 8 cm, 11 cm
- Add the sides. Add every side to get the perimeter.15 + 5 + 7 + 6 + 8 + 11 = 52
- Write the answer. 52 cm
Check. 2 × (15 + 11) = 52 cm. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 3 cm by 2 cm, so the sides are 4 cm, 5 cm and so on.6 - 2 = 4, 8 - 3 = 5
- List the six sides. An L-shape has six straight sides.8 cm, 4 cm, 3 cm, 2 cm, 5 cm, 6 cm
- Add the sides. Add every side to get the perimeter.8 + 4 + 3 + 2 + 5 + 6 = 28
- Write the answer. 28 cm
Check. 2 × (8 + 6) = 28 cm. ✓
Method. Find the missing sides, then add all six.
- Find the missing lengths. The notch is 10 cm by 8 cm, so the sides are 4 cm, 6 cm and so on.12 - 8 = 4, 16 - 10 = 6
- List the six sides. An L-shape has six straight sides.16 cm, 4 cm, 10 cm, 8 cm, 6 cm, 12 cm
- Add the sides. Add every side to get the perimeter.16 + 4 + 10 + 8 + 6 + 12 = 56
- Write the answer. 56 cm
Check. 2 × (16 + 12) = 56 cm. ✓
Method. Find the missing sides, then add.
- Find the missing lengths. The notch is 4 cm by 2 cm, so the sides are 4 cm, 6 cm and so on.6 - 2 = 4, 10 - 4 = 6
- List the six sides. An L-shape has six straight sides.10 cm, 4 cm, 4 cm, 2 cm, 6 cm, 6 cm
- Add the sides. Add every side to get the perimeter.10 + 4 + 4 + 2 + 6 + 6 = 32
- Write the answer. 32 m
Check. 2 × (10 + 6) = 32 m. ✓
Method. Add all six sides.
- Find the missing lengths. The notch is 3 cm by 2 cm, so the sides are 3 cm, 4 cm and so on.5 - 2 = 3, 7 - 3 = 4
- List the six sides. An L-shape has six straight sides.7 cm, 3 cm, 3 cm, 2 cm, 4 cm, 5 cm
- Add the sides. Add every side to get the perimeter.7 + 3 + 3 + 2 + 4 + 5 = 24
- Write the answer. 24 cm
Check. Ali is wrong: the perimeter is 24 cm. ✓
Method. Work out the perimeter of each shape.
- Rectangle. 2 × (6 + 4) = 20 cm.20 cm
- L-shape. The L-shape has the same perimeter as its outside rectangle, so it is also 20 cm.20 cm
- Write the answer. Yes
Check. They are equal, so the answer is Yes. ✓
Watch out. An L-shape with a corner removed has the same perimeter as the rectangle.
Method. Look at the sides that are added and the sides that are removed.
- Look at one notch. The notch takes away a length from one side but adds the same length to another.same total
- Compare. The perimeter is the same as the rectangle.same perimeter
- Write the answer. Because the notch adds the same length in one direction as it takes away in the other, so the total around the outside is the same.
Check. 10 + 6 = 16 both ways. ✓