Math // Measurement

Perimeter of Compound Shapes

Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

If the learner is given an L-shaped garden plan with all the side measurements labelled, can they add all the sides together to find the total perimeter?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Find the perimeter of an L-shaped figure by identifying all side lengths
  • Calculate the perimeter of a composite shape where some sides must be deduced
  • Draw a composite rectilinear shape with a perimeter of 40 cm

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Perimeters of polygonsRequired

    Measurement // Ages 8 to 9

    Y4 perimeter of polygons is prerequisite to composite rectilinear perimeter

  • Area of compound shapesHelpful

    Measurement // Ages 8 to 9

    Decomposing rectilinear figures supports finding missing sides for perimeter

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Perimeter of Compound Shapes

Ages 9 to 10 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Measurement

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Year 5 pupils measure and calculate the perimeter of composite rectilinear shapes (straight sides, with every corner made by sides meeting at right angles — rectangles joined, e.g. an L-shape). The distinctive skill is DEDUCING unmarked side lengths from the labelled ones: in each direction, the side lengths on one side of the shape add up to the side lengths on the opposite side. In an L-shape this means the two shorter sides along one direction add up to the opposite longer side (so a missing length is found by adding the two shorter sides, or by subtracting a known shorter side from the longer one); other shapes, such as U- or T-shapes, may have more than two parts on one side. Pupils then total every boundary side exactly once. Chief hazards: adding only the given numbers (forgetting missing sides), working out a missing length wrongly, including internal split-lines, double-counting a side, and confusing perimeter (a length in cm or m) with area (cm2 or m2).

Common misconceptions

  • Forgets to find the unmarked sides and adds only the given numbers.
  • Cannot see that the two shorter sides equal the opposite longer side, so mis-deduces a missing length.
  • Includes internal lines, double-counts a side, or confuses perimeter with area.

Useful representations

  • L-shaped / rectilinear figure with some sides unmarked
  • Missing-side deduction (opposite sides equal)
  • Tick-each-side-as-counted method
  • Boundary-versus-internal-line contrast

Teaching practices

  • Define a rectilinear/compound shape (straight sides, right angles; rectangles joined) and use both terms.
  • Deduce unmarked sides from labelled ones: the two shorter sides along a direction sum to the opposite longer side (add or subtract known lengths).
  • Mark each side as it is added so none is missed or counted twice, and check every side is included.
  • Distinguish the boundary (perimeter) from internal split-lines, which are not part of the perimeter.
  • Keep perimeter (length, cm) distinct from area (cm²).

Activities to try

  1. 1

    Trace-the-boundary L-shape with live missing-side reveal

    Why it works: A hidden side length is not missing information: it can be recovered from the labelled sides, because the shorter sides along a direction add up to the opposite longer side. Perimeter is the total distance around the boundary, each side counted exactly once, excluding internal lines.

    1. Trace a finger (or pen) all the way around the boundary of an L-shaped figure, naming or ticking each side as you pass it so no side is counted twice and none is missed.
    2. When you reach an unmarked side, work out its length from the labelled sides: the two shorter sides along a direction add up to the opposite longer side, so find a missing longer side by adding the two shorters, or find a missing shorter side by subtracting the known shorter length from the longer. Write the deduced length on the blank.
    3. Keep a running total as you go; when every side is ticked, read off the perimeter in cm.
    4. Notice the internal 'fold' line where the rectangles join: leave it out — it is not part of the boundary.
  2. 2

    Find-the-missing-side, total, and spot-the-mistake

    Why it works: The method has two stages — deduce all unknown sides, then add every boundary side once — and the common errors (adding only given numbers, including inside lines, double-counting, giving area instead) are specific and checkable.

    1. Given an L-shape with some sides labelled and some blank, find each unmarked side by adding or subtracting the labelled lengths along that direction, then total the whole perimeter.
    2. Examine a worked solution where a character has made an error — e.g. included an internal join-line, or omitted an unmarked side — and say exactly which side is wrong and what the correct total should be.
    3. Decompose the shape into rectangles to see why the two shorter sides add up to the opposite longer side.
  3. 3

    Draw a composite shape to a target perimeter

    Why it works: Constructing a shape to a given perimeter — not just reading one — requires the pupil to control which sides are boundary, how deduced sides relate, and to keep length (cm) distinct from area.

    1. On cm paper, draw a composite rectilinear shape (rectangles joined, straight sides that always meet at right angles) whose perimeter is exactly 40 cm.
    2. Label every side and check that the total length across the shape in each direction balances.
    3. Add all the boundary sides to confirm the total is 40 cm, ticking each side once.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/3.1c

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