Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Of All the Areas

Or search by topic

Age 14 to 16

Challenge Level

*Of All the Areas printable sheet*

*You may wish to print off some isometric paper or use the isometric dotty grid environment for this problem.*

*This problem follows on from Isometric Areas and More Isometric Areas.*

When working on an isometric grid, we can measure areas in terms of equilateral triangles instead of squares.

Here are some equilateral triangles.

If the area of the smallest triangle is 1 unit, what are the areas of the other triangles?

**Can you see a relationship between the area and the length of the base of each triangle?
Will the pattern continue?
Can you explain why?**

All the triangles in the first image had horizontal bases, but it is also possible to draw "tilted" equilateral triangles.

These triangles all have a "tilt" of 1.

Can you explain why your rule works?

What about areas of triangles with other "tilts"?