Perimeter (age 10+)
Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically
What a learner can do afterwards
- Draw two rectangles with area 24 cm² but different perimeters
- Find two shapes with perimeter 20 cm but different areas
- Explain why a long thin rectangle and a square can have the same area but different perimeters
The lesson
Area tells you how much space is inside a shape. Perimeter tells you the distance all the way around its edge. You might expect that when one changes, the other changes too, but that is not always true. Two shapes can share the same area and still have completely different perimeters.
Now look at a rectangle that is 3 units by 8 units. Its area is 3 x 8 = 24 square units, the same as before. But its perimeter is 3 + 8 + 3 + 8 = 22 units, two units more than the first rectangle.
Rectangles shaped more like a square usually have a smaller perimeter than long, thin rectangles with the same area. When you compare two shapes, always check area and perimeter separately. Matching one does not mean the other matches too.
Same area does not mean same perimeter, and same perimeter does not mean same area, so check each one on its own.
Watch it
Where it sits
Learn first
This opens up
Nothing builds on it yet.
Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.