lesson
Area does not determine perimeter
1 · Learn
Area measures a region; perimeter measures its boundary. Rectangles can share an area yet have different perimeters. Conversely, equal perimeters do not guarantee equal areas.
Calculate both quantities from the dimensions instead of assuming one determines the other. Use square units for area and length units for perimeter, even when their numerical values happen to match.
2 · Worked example
A 6 cm by 4 cm rectangle and an 8 cm by 3 cm rectangle both have area 24 cm², but their perimeters are 20 cm and 22 cm.
3 · Your turn
Compare 7 cm by 3 cm and 6 cm by 4 cm rectangles. Find each area and perimeter.
Check your answer
The areas are 21 cm² and 24 cm². Both perimeters are 20 cm, showing equal perimeter with different area.
4 · Apply your learning
Use squared paper to find three rectangles of one chosen area and explain how their boundaries differ.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress