Idea 16of 22Builds onTwo lengths and two widths
Same area, different perimeters
Can two gardens cover the same ground but need different fences?
Today you'll discover
- three gardens with one area
- how their fences compare
- why a thin shape has more edge
Think firstThree gardens, each 12 m²
All three gardens cover 12 m². Do they need the same length of fence?
Decide first, then press Next. Compare the green lines, then the orange ones.
Three rectangles drawn to one scale: 12 m by 1 m, 6 m by 2 m and 4 m by 3 m. Squares fill each one and each is marked area 12 m². Orange lines trace their edges, marked perimeter 26 m, 16 m and 14 m. The 4 by 3 is ringed in green as least fence and the 12 by 1 in orange as most fence. The last step shows four gardens of 24 m².
See the whole ideathe big idea and the key word, in one place
The big idea
Shapes with the same area can have different perimeters.
Twelve square metres, three fences
Three gardens of 12 m², three different fences.
- 12 by 126 m
- 6 by 216 m
- 4 by 314 m
Why it happensA thin shape puts every square against the edge. A squarer one tucks squares into the middle, away from the fence.
Key word
- dimensions
- the length and width of a shape, like 6 m by 2 m
Ready to use it?
- Show two rectangles with the same area and different perimeters.