Length and Perimeter

Section: Measurement | Syllabus: Cambridge Primary Mathematics (0845)

Units of Length and Perimeter

Length can be measured in millimetres (mm), centimetres (cm), metres (m) or kilometres (km) - choose a sensible unit for the size of the object or distance.
- 10 mm = 1 cm
- 100 cm = 1 m
- 1000 m = 1 km
Before adding or comparing lengths, make sure they are all written in the same unit first.
The perimeter of a shape is the total distance all the way around its outside edge - found by adding the lengths of every side.

The dashed perimeter path goes around all four sides: 2 × (length + width)

Question: A rectangle has a length of 9 cm and a width of 4 cm. Find its perimeter.
- Step 1: Add the length and width: 9 + 4 = 13
- Step 2: Double this total, since each side appears twice: 13 × 2 = 26
- Answer: Perimeter = 26 cm

A compound shape is made from two or more rectangles or squares joined together.
Some side lengths are not always labelled - use the sides you are given to work out any missing sides before adding everything up.
Opposite sides of a rectangle are equal, so a missing length can often be found by adding or subtracting the labelled sides around it.

The missing side is found by subtracting the square's side from the rectangle's width: 12 − 5 = 7 cm

Question: A square of side 5 cm sits on the left end of a rectangle that is 12 cm wide and 6 cm tall, flush with the rectangle's left side and top edge. Find the perimeter of the whole compound shape.
- Step 1: Mark every outside side, including the exposed part of the rectangle's top edge to the right of the square: 12 − 5 = 7 cm.
- Step 2: List all seven outer sides going around the shape: 6 (rectangle's left side) + 5 (square's left side) + 5 (square's top) + 5 (square's right side) + 7 (exposed rectangle top) + 6 (rectangle's right side) + 12 (rectangle's bottom).
- Step 3: Add them all together: 6 + 5 + 5 + 5 + 7 + 6 + 12 = 46
- Answer: Perimeter = 46 cm

When two shapes are joined edge-to-edge, the shared edge is hidden inside the new shape and is no longer part of its perimeter.
Joining shapes does not mean adding their separate perimeters together - the perimeter of the combined shape is less than that total.
Shapes made from the same number of unit squares can still have different perimeters, depending on how many edges are shared internally.

The shared edge (dashed) is hidden inside the joined rectangle and is no longer part of its perimeter

Question: Two squares, each 1 cm × 1 cm, are joined edge-to-edge to make a 2 cm × 1 cm rectangle. Each separate square has a perimeter of 4 cm. Find the perimeter of the joined rectangle.
- Step 1: The two separate perimeters add up to 4 + 4 = 8 cm.
- Step 2: One 1 cm edge from each square is now shared and hidden inside the rectangle, so subtract it twice: 8 − 1 − 1 = 6
- Step 3: Check directly using the rectangle formula: 2 × (2 + 1) = 6
- Answer: Perimeter = 6 cm

MistakeLeaving out a missing side in a compound shape instead of working it out first

Fixuse the labelled sides to calculate every missing length before adding them all up

MistakeAdding the two shapes' separate perimeters together when they are joined

Fixsubtract the shared edge twice, since it is hidden inside the joined shape and no longer on the outside

MistakeUsing length × width when asked for perimeter

Fixperimeter is a sum of side lengths (cm); length × width gives the area (cm²) instead - check what the question is asking for

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