Maths · KS3 and GCSE · Interactive lesson
Area, perimeter and volume
Trace a rectangle’s boundary, count square units and stack cubes. Explore rectangle and triangle areas, then the volume of a cuboid.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Find a rectangle’s perimeter (distance around it) and area (space inside it).
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- A rectangle’s area counts the square units that cover its inside.
- A rectangle’s perimeter is the total of its four side lengths.
- Area and perimeter measure different things, so they use different units.
Useful starting points
These lessons open in a new tab so you can return here.
What do the words mean?
- Perimeter
- The total distance around the outside boundary.
- Area
- How much flat surface is covered.
- cm²
- A square centimetre: the area of a 1 cm by 1 cm square.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the width the same. Change the length. Compare the boundary measurement with the number of square units inside.
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
The purple tiles cover the area. Each tile is 1 cm². The orange line follows the perimeter. Opposite sides of a rectangle have equal lengths. The picture resizes to fit: compare the labelled lengths and count the tiles.
More about this diagram
Still picture. Play particle motion in Stage 2.
12 square tiles inside · 14 cm around
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- Each row contains 4 square tiles. There are 3 rows.
- The inside contains 3 × 4 = 12 tiles: area 12 cm².
- Trace the orange edge: 4, 3, 4, then 3 cm.
- Add these lengths: 4 + 3 + 4 + 3 = 14 cm around.
Try on your own
Your turn. No rush.
Question 1
A rectangle has 3 rows of 4 tiles. Each tile covers 1 cm². What is the rectangle’s area?
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
A good place to pause
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Can you explain the difference between distance around a shape and space inside it, including their units?
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
Topic labels and your lesson-view preference are saved in this browser. This tab also remembers the last lesson stage, so you can choose to continue there. If you choose revision, selected activities and suggested revisit dates are saved here too. Recent question codes are also kept to reduce repeats. Reflection notes are saved automatically per topic when you type them; you can delete a note in the recap. They stay in this browser and are visible to other people using it. Practice answers and enquiry details are not saved. Clearing browser data removes the labels.