The idea in brief. An area is the two sides multiplied and a perimeter is the four sides added, so each one can be run backwards: divide by the side you have, or take the side you have off the perimeter TWICE and halve what is left. Given a perimeter and one side, write the word equation first: 2 times breadth equals the perimeter minus two lengths, and only then halve. In the lesson. You have found the perimeter of a rectangle by adding all four sides. Today, we will work backwards from area or perimeter to find a missing side. From the perimeter, subtract both lengths, then divide by 2. From the area, divide by the side you know.
Lesson video, with the working
Find a missing side
3 min 29 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
How do you find a missing side from area or perimeter in P3?
This Primary 3 subtopic runs the area and perimeter rules backwards.
What your child learns here
This Primary 3 subtopic runs the area and perimeter rules backwards. It applies the syllabus outcomes on the perimeter and area of a rectangle or square to questions that give the total and ask for one side.
A rectangle's perimeter is made of 2 lengths and 2 breadths, so both copies of a known side must come off.
What is left after that is two equal sides, so it is halved.
Area is length × breadth, so a missing side is the area divided by the side you know.
A square's side can be found from its perimeter by dividing by 4.
Does the answer make sense?
When a rectangle's perimeter is given and one side is asked for, that side must be less than half the perimeter, because one length and one breadth together make exactly half. Then your child can check the unit matches the question: a side or perimeter in cm, an area in cm².
How to practise these questions
The Basic questions practise finding a side by dividing the area by the known side. The Intermediate questions add moving between area and perimeter, such as finding a perimeter from an area, or cutting a square into equal squares. The Challenge questions link area and perimeter, so one is used to reach the other. If a missing side question stalls, watch the solution film for it and come back to it later from Revision.
Questions parents ask
Is finding a missing side in the P3 syllabus? The Primary 3 syllabus covers the perimeter and area of a rectangle or square. Finding one side from a given area or perimeter is listed by name in the following year's syllabus, so this page uses the P3 rules worked backwards as an early step.
Why do we subtract the length twice? A rectangle has two lengths and two breadths. The perimeter includes both lengths, so both come off before what is left is shared between the two breadths.
How do I find the side of a square from its perimeter? All four sides of a square are equal, so divide the perimeter by 4. A square with a perimeter of 28 cm has sides of 7 cm.
