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Academy11+

11+ Maths · Topic explained

Perimeter

How much fence do you need to go all the way round a garden?

The big idea

Perimeter is the total distance all the way round the outside of a shape.

Picture it

Like walking round the edge of a field and adding up every side.

Key words

perimeter
The distance all the way round a shape.
length
How long a side is, in cm or m.
rectilinear
Made of straight sides meeting at right angles, like an L shape.

Worked examples

  1. 1Warm-up

    Find the perimeter of a rectangle 8 cm long and 3 cm wide.

    • 8 + 3 + 8 + 3 = 22 cm
    • Or (8 + 3) × 2 = 22 cm
  2. 211+ standard

    Find the perimeter of this L-shape.

    • Missing sides: 10 − 6 = 4 and 8 − 4 = 4
    • 10 + 4 + 4 + 4 + 6 + 8 = 36 cm
  3. 311+ standard

    A square has a perimeter of 36 cm. How long is each side?

    • A square has 4 equal sides
    • 36 ÷ 4 = 9 cm
  4. 411+ standard

    A rectangle has a perimeter of 30 cm and a length of 9 cm. Find its width.

    • Two lengths: 9 × 2 = 18
    • 30 − 18 = 12 for the two widths
    • 12 ÷ 2 = 6 cm

The common mistake

The mistake

Perimeter of an 8 cm by 3 cm rectangle = 8 + 3 = 11 cm.

Instead

Add all four sides: 8 + 3 + 8 + 3 = 22 cm.

Why: Only two sides are labelled, but the shape has four. The unlabelled ones still count.

Where it comes up in the 11+

Rectangles, L-shapes with missing sides, and working backwards from a perimeter.

The video

Video coming soon

We're making a short video that explains perimeter step by step. Until then, everything it covers is on this page.

Free printable

Perimeter worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. What is the perimeter of a square with sides of 5 cm?

    • 10 cm
    • 20 cm
    • 25 cm
    • 15 cm
    Show the answer

    20 cm

    4 sides × 5 cm = 20 cm.

  2. 2. What is the perimeter of a rectangle 12 m long and 5 m wide?

    • 17 m
    • 34 m
    • 60 m
    • 29 m
    Show the answer

    34 m

    (12 + 5) × 2 = 34 m.

  3. 3. An equilateral triangle has a perimeter of 27 cm. How long is each side?

    • 9 cm
    • 7 cm
    • 13.5 cm
    • 81 cm
    Show the answer

    9 cm

    3 equal sides: 27 ÷ 3 = 9 cm.