Understanding how areas and perimeters change as we change a shape is important not just mathematically but also in solving many real-life problems. This collection of rich tasks is intended to help you to develop these useful insights into area and perimeter.
problem
Perimeter possibilities
Age
11 to 14
Challenge level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
problem
Changing areas, changing perimeters
Age
11 to 14
Challenge level
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
problem
Fence it
Age
11 to 14
Challenge level
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
problem
Isosceles triangles
Age
11 to 14
Challenge level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
problem
Curvy areas
Age
14 to 16
Challenge level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?