Area and perimeter
Area is how many squares fit inside. Perimeter is how far it is round the edge. Change the sides and the two numbers go their own separate ways.
Area 4 × 3 = 12 squares
Perimeter 2 × (4 + 3) = 14 units
Drag the ringed corner to resize the rectangle.
Same fence, different area
Ready to try some? Area & perimeter worksheets
Where it usually goes wrong
Area and perimeter get used as two words for “big”. They are two different measurements of one shape and they do not move together: 9 × 1 and 5 × 5 are both 20 units round the edge, and one holds nine squares while the other holds twenty-five. Asked to fence a garden, the child who thinks these are the same thing builds the wrong garden.
Try this
- Press 9 × 1, then 8 × 2, then 5 × 5. The perimeter reads 20 every time and the area goes 9, 16, 25.
- Drag the corner and watch which number changes faster. Adding one to a side adds two to the perimeter and adds a whole row to the area.
- Find the rectangle with the most area for a perimeter of 20. It is the square, and that is true of every perimeter.
Where this goes next
The same trap turns up one dimension higher in Inside and Outside a Box, where what a box holds and what it takes to wrap it also refuse to keep step.