Idea 18of 22Builds onClose to a square needs the least fence
Same perimeter, different areas
Can the same fence hold different amounts of space?
Today you'll discover
- five shapes from one rope
- how much each one holds
- which shape holds the most
Think firstFive rectangles made from 20 m of rope
Each uses 20 m of rope. Which holds the most space inside?
Decide first, then press Next. Compare the green lines, then the orange ones.
Five rectangles drawn to one scale: 9 by 1, 8 by 2, 7 by 3, 6 by 4 and 5 by 5 metres. Orange lines trace each edge, each marked perimeter 20 m. Squares fill them, marked area 9, 16, 21, 24 and 25 m². The 5 by 5 is ringed in green as most space inside, the 9 by 1 in orange as least. The last step shows three pens made from 12 m of fence.
See the whole ideathe big idea and the key word, in one place
The big idea
Shapes with the same perimeter can have different areas; the squarest holds the most.
Compare themSame area: the squarest needs the least fence. Same fence: the squarest holds the most space.
For example20 m of rope makes a 9 m by 1 m pen (9 m²) or a 5 m by 5 m pen (25 m²).
Key word
- greatest area
- the most space a shape can cover, compared with the others
Ready to use it?
- Show two rectangles with the same perimeter and different areas.