Year 5: Perimeter of rectangles and composite shapes
Part of the Year 5 units, perimeter, area, volume and time chapter. Chapter overview · whole chapter on one page
Perimeter of rectangles and composite shapes
The perimeter is the distance all the way round the outside of a shape. To find it, add the lengths of every outside side.
A rectilinear shape has only square corners. A composite shape is made from rectangles joined together, like the L-shape below. Some of its sides are not labelled. In a rectilinear shape, the sides can be found by subtracting: the top of the L-shape is the bottom length minus the width of the notch.
Key ideas
- The perimeter is the total length of the outside sides. Each outside side is counted once.
- Rectangle: perimeter = length + width + length + width, or 2 × (length + width).
- Missing side in a rectilinear shape: take away the known sides from a longer side.
- Check: an L-shape has the same perimeter as the rectangle that goes around it.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 7 cm, 4 cm, 7 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 4 + 7 + 4 = 22 cm
- Write the answer. 22 cm
Check. The shortcut gives the same answer: 2 × (7 + 4) = 22 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (3 cm).8 − 3 = 5 cm
- Find the missing inside side. The left side is 6 cm tall. The lower right side is 3 cm, so the rest is the inside side.6 − 3 = 3 cm
- Add all six outside sides. Go all the way round the shape once and add each side.8 + 3 + 3 + 3 + 5 + 6 = 28 cm
- Write the answer. 28 cm
Check. Shortcut for an L-shape: 2 × (8 + 6) = 28 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 2.5 m, 1.2 m, 2.5 m, 1.2 m
- Add the lengths of the sides. Add one side at a time and keep the unit.2.5 + 1.2 + 2.5 + 1.2 = 7.4 m
- Write the answer. 7.4 m
Check. The shortcut gives the same answer: 2 × (2.5 + 1.2) = 7.4 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Watch out
Do not add the lines inside a shape, and do not forget a side. Count every outside side once. For the L-shape, there are six outside sides, not four.Exercise 8C Perimeter of shapes
Non-calculatorKey words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 9 cm, 4 cm, 9 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.9 + 4 + 9 + 4 = 26 cm
- Write the answer. 26 cm
Check. The shortcut gives the same answer: 2 × (9 + 4) = 26 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 7 cm, 7 cm, 7 cm, 7 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 7 + 7 + 7 = 28 cm
- Write the answer. 28 cm
Check. The shortcut gives the same answer: 2 × (7 + 7) = 28 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 12 cm, 5 cm, 12 cm, 5 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.12 + 5 + 12 + 5 = 34 cm
- Write the answer. 34 cm
Check. The shortcut gives the same answer: 2 × (12 + 5) = 34 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 8.5 cm, 3 cm, 8.5 cm, 3 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.8.5 + 3 + 8.5 + 3 = 23 cm
- Write the answer. 23 cm
Check. The shortcut gives the same answer: 2 × (8.5 + 3) = 23 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 3.5 m, 2 m, 3.5 m, 2 m
- Add the lengths of the sides. Add one side at a time and keep the unit.3.5 + 2 + 3.5 + 2 = 11 m
- Write the answer. 11 m
Check. The shortcut gives the same answer: 2 × (3.5 + 2) = 11 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 4.2 m, 1.6 m, 4.2 m, 1.6 m
- Add the lengths of the sides. Add one side at a time and keep the unit.4.2 + 1.6 + 4.2 + 1.6 = 11.6 m
- Write the answer. 11.6 m
Check. The shortcut gives the same answer: 2 × (4.2 + 1.6) = 11.6 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 0.8 m, 0.8 m, 0.8 m, 0.8 m
- Add the lengths of the sides. Add one side at a time and keep the unit.0.8 + 0.8 + 0.8 + 0.8 = 3.2 m
- Write the answer. 3.2 m
Check. The shortcut gives the same answer: 2 × (0.8 + 0.8) = 3.2 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.6 sides: 7 cm, 3 cm, 2 cm, 2 cm, 5 cm, 5 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 3 + 2 + 2 + 5 + 5 = 24 cm
- Write the answer. 24 cm
Check. The shortcut 2 × (7 + 5) = 24 cm agrees. ✓
Watch out. Do not add the lines inside a shape, and do not miss out a side.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (4 cm).10 − 4 = 6 cm
- Find the missing inside side. The left side is 7 cm tall. The lower right side is 4 cm, so the rest is the inside side.7 − 4 = 3 cm
- Add all six outside sides. Go all the way round the shape once and add each side.10 + 4 + 4 + 3 + 6 + 7 = 34 cm
- Write the answer. 34 cm
Check. Shortcut for an L-shape: 2 × (10 + 7) = 34 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Half the perimeter is one length plus one width.
- Find half the perimeter. A rectangle has two lengths and two widths, so half of the perimeter is one length plus one width.30 ÷ 2 = 15 cm
- Take away the known side. The other side is what is left of the 15 cm.15 − 9 = 6
- Write the answer. 6 cm
Check. 9 + 6 = 15, and 2 × 15 = 30. ✓
Watch out. Do not subtract 9 from 30 and stop. That gives the two sides together, not one side.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. A square has four equal sides, so divide the perimeter by 4.
- Share the perimeter between the four sides. All four sides of a square are the same length.36 ÷ 4 = 9
- Write the answer. 9 cm
Check. 9 + 9 + 9 + 9 = 36. ✓
Watch out. Divide by 4, not by 2. Two would be right for a rectangle, but not for a square.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the perimeter of each rectangle, then compare.
- Find the perimeter of the first rectangle. Add all four sides.6 + 2 + 6 + 2 = 16 cm
- Find the perimeter of the second rectangle. Add all four sides.5 + 3 + 5 + 3 = 16 cm
- Write the answer. The two perimeters are the same.Neither. Both have a perimeter of 16 cm.
Check. Both shapes add up to 16 cm. ✓
Watch out. Rectangles with different sides can have the same perimeter.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the perimeter of the field, then multiply by the number of laps.
- Find the perimeter of one lap. One lap goes all the way round the field.2 × (45 + 30) = 150 m
- Multiply by 3 laps. Three laps is three times the perimeter.150 × 3 = 450 m
- Write the answer. 450 m
Check. 150 m + 150 m + 150 m = 450 m. ✓
Watch out. Find the perimeter of one lap first. Then multiply by the number of laps.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Half the perimeter is one length plus one width. Then take away the length.
- Find half the perimeter. Half of the perimeter is one length plus one width.10.4 ÷ 2 = 5.2 m
- Take away the length. What is left is the width.5.2 − 3.2 = 2 m
- Write the answer. 2 m
Check. 3.2 + 2 = 5.2, and 2 × 5.2 = 10.4. ✓
Watch out. Halve the perimeter first. Do not subtract 3.2 from 10.4 and stop.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (4 cm).9 − 4 = 5 cm
- Find the missing inside side. The left side is 5 cm tall. The lower right side is 3 cm, so the rest is the inside side.5 − 3 = 2 cm
- Add all six outside sides. Go all the way round the shape once and add each side.9 + 3 + 4 + 2 + 5 + 5 = 28 cm
- Write the answer. 28 cm
Check. Shortcut for an L-shape: 2 × (9 + 5) = 28 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.6 sides: 4 cm, 2 cm, 2 cm, 2 cm, 2 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.4 + 2 + 2 + 2 + 2 + 4 = 16 cm
- Write the answer. 16 cm
Check. Cutting the corner changes the shape, but not the total outside length. ✓
Watch out. When a corner square is cut out, the cut-out edges replace the edges that were removed. The total does not change.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Use the rectangle with length 3 times its width. Share the half-perimeter into four equal widths.
- Write the length in terms of the width. The length is three widths, so one length and one width make four widths.length + width = 4 widths
- Find half the perimeter. Half of the perimeter is one length plus one width.48 ÷ 2 = 24 cm
- Find the width. The 24 cm is 4 widths, so one width is 24 ÷ 4.24 ÷ 4 = 6 cm
- Find the length. The length is three times the width.3 × 6 = 18 cm
Check. 18 + 6 = 24, and 2 × 24 = 48. ✓
Watch out. Find the width first, then multiply it by 3 to find the length.