Areas and Integrals

Areas and Integrals

Integration can be better understood if you consider its relationship with area. All of the problems in this feature require you to think deeply about area, integrals, and the relationship between them.


Towering Trapeziums 

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

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?

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?
A collection of short Stage 4 problems on area and volume.