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
1 · Read
You already know how to find a perimeter by adding every outside edge. Area tells you how much space is inside a shape. That helps when two rugs cover the same floor but need different lengths of edge trim. Two shapes can share the same area and still have different perimeters. In a rectangle, a length plus a width equals half the perimeter.
Now look at a rectangle that is 3 cm by 12 cm. Its area is 3 x 12 = 36 square cm, the same as before, but its perimeter is 30 cm, four more. For two rectangles with the same area, the one closer to a square always has the smaller perimeter. The same perimeter can hide different areas: a 4 by 9 and a 6 by 7 rectangle both go around 26 cm, but their areas are 36 and 42 square cm.
For the same area, a rectangle shaped more like a square always has a smaller perimeter than a long, thin one. When you compare two shapes, 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.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
18 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.