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Perimeter

FoundationChallengeAQAEdexcelOCR

Get to grips with perimeter using these Foundation GCSE Maths practice questions. The worksheet focuses on calculating perimeter, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Perimeter is the total distance around the edge of a shape.

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Topic overview

Perimeter is the total distance around the outside of a two-dimensional shape. You find it by adding the lengths of all the sides.

For a rectangle this shortcuts to \(2(l + w)\), since opposite sides are equal. For any irregular shape, simply add every side in turn, working around the outline so none is missed.

Compound shapes often leave some sides unlabelled, and those must be worked out from the others before adding. Because perimeter is a length, the units are ordinary units such as centimetres, never squared ones.

Revision notes

Finding perimeter

Add every side. Work around the shape in one direction so no side is counted twice or missed.

For a rectangle \(8\)cm by \(5\)cm: \(8 + 5 + 8 + 5 = 26\)cm, or \(2(8 + 5) = 26\)cm.

Missing sides on compound shapes

Unlabelled sides can be found from the labelled ones, because opposite sides of the overall shape must match.

If the total width is \(10\)cm and one section is \(6\)cm, the remaining section is \(4\)cm.

Units

Perimeter is a length, so the units are cm, m or km, never squared.

Mixing units within a shape is a common trap, so convert everything before adding.

Key points

  • Perimeter is the distance around a shape.
  • Add the lengths of all the sides.
  • A rectangle's perimeter is \(2(l + w)\).
  • Work out unlabelled sides first.
  • Units are ordinary lengths, not squared.
  • Convert to the same units before adding.

Worked examples

Example 1

Find the perimeter of a rectangle \(12\)cm by \(7\)cm.

Working

\[2 \times (12 + 7)\]opposite sides are equal
\[2 \times 19\]add the length and width first
\[= 38\text{cm}\]state the perimeter with units

Example 2

A triangle has sides \(6\)cm, \(8\)cm and \(11\)cm. Find its perimeter.

Working

\[6 + 8 + 11\]add all three sides
\[= 25\text{cm}\]state the perimeter

Example 3

A compound shape has a total width of \(15\)cm, with one section \(9\)cm. Find the missing section.

Working

\[15 - 9\]subtract the known section from the total
\[= 6\text{cm}\]state the missing length

Common mistakes

  • Using squared units.

    Perimeter is a length, so cm not cm². Squared units belong to area.

  • Missing a side on a compound shape.

    Work around the outline systematically and mark each side as you add it.

  • Forgetting to work out unlabelled sides.

    Every side must be known before the perimeter can be found.

  • Mixing centimetres and metres.

    Convert to one unit before adding.

Exam tips

  • Work around the shape in one direction, ticking off each side.
  • Find any missing sides before you start adding.
  • Use ordinary length units, never squared.
  • Check the total looks sensible for the size of the shape.

Key terms

Perimeter
The total distance around a shape.
Compound shape
A shape made from simpler shapes joined together.
Length
A one-dimensional measurement.
Convert
To change between units.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.