Areas of Interest

Areas of Interest

In this feature, we offer a selection of rich problems about area for use in all secondary classrooms.

We start by inviting younger students to explore areas on isometric grids, move on to problems about Pythagoras' theorem, and finally, for the oldest students, we offer tasks about integration and functional relationships.


Isometric Areas 

Age 11 to 14 Challenge Level:
We usually use squares to measure area, but what if we use triangles instead?

More Isometric Areas 

Age 11 to 14 Challenge Level:
Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

Of All the Areas 

Age 14 to 16 Challenge Level:
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Towering Trapeziums 

Age 14 to 16 Challenge Level:
Can you find the areas of the trapezia in this sequence?

Graphs of Changing Areas 

Age 16 to 18 Challenge Level:
Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

Area L 

Age 16 to 18 Challenge Level:
By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?