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.
Lesson video, with the working
Finding a side from the perimeter
3 min 31 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How can I help my child with finding a missing side?
A known area or perimeter can tell your child about a length that has not been printed on the figure.
What your child learns here
A known area or perimeter can tell your child about a length that has not been printed on the figure. The Primary 4 syllabus includes finding a rectangle's dimension from the other dimension and its area or perimeter, and finding a square's side from its area or perimeter. Your child first identifies which measurement is given, then reverses the appropriate calculation.
Find an unknown rectangle dimension by dividing its area by the known dimension, with both lengths expressed in compatible units.
Halve a rectangle's perimeter to obtain length plus breadth, then subtract the known dimension to find the other one.
Use four equal sides to find a square's side from its perimeter, or find two equal factors of its area.
Write a side length in a length unit such as cm or m, even when the starting information is an area in square units.
Does the answer make sense?
For a rectangle with area 56 cm² and one side 8 cm, a proposed missing side of 7 cm gives 8 × 7 = 56 cm². Multiplying the two lengths back together must recover the stated area; this also checks that your child has answered with a length rather than another area.
How to practise these questions
Basic questions include counting whole and half grid squares, finding a rectangle's length from area and moving from a square's area to its perimeter. Intermediate work links an area to a perimeter or compares a square and rectangle made with equal boundary lengths. Challenge questions involve frames, a removed square or wire reshaped into several squares. Your child should identify the quantity that stays the same in each situation before working backwards. For a cut-out, establish the original area before using the rectangle relationship; for a wire, account for the full length used. After checking the solution, ask your child to explain why the first operation follows from the information supplied.
Questions parents ask
Why is half the rectangle's perimeter useful? The full boundary contains two lengths and two breadths. Halving that total leaves one length plus one breadth, so knowing either lets your child find the other by subtraction. Asking what half the perimeter represents helps the arithmetic stay connected to the rectangle. Halving alone does not usually give an individual side.
Does my child need a square-root method for a square's side? For whole-number side lengths, your child can use multiplication facts or equal factor pairs to identify the number multiplied by itself. For example, the required side is the equal factor whose product matches the given area. The useful reasoning is that a square has equal length and breadth; introducing a new notation is unnecessary for these whole-number cases.
Can equal perimeters mean equal areas? They can, but equal perimeters alone do not guarantee equal areas. Two rectangles can use the same total boundary length while having different pairs of dimensions. When a question compares figures made from the same length of wire, your child should find each required side or area from the given shape information rather than transferring every measurement between the figures.
