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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Areas and Integrals

### Towering Trapeziums

### Of All the Areas

### Graphs of Changing Areas

### Area L

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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.

Age 14 to 16

Challenge Level

Can you find the areas of the trapezia in this sequence?

Age 14 to 16

Challenge Level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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...

Age 16 to 18

Challenge Level

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?