Challenge Level

*This problem follows on from Isometric Areas.*

*You may wish to print off some isometric paper.*

Here is an equilateral triangle with sides of length 1.

Let's define a unit of area, $T$, such that the triangle has area $1T$.

Each of the triangles below has at least two edges whose side lengths are whole numbers.

For example triangle $B$ has sides of length $3$ and $4$.

Work out the area, in terms of $T$, of each of the triangles.

Compare the areas to the whole number side lengths.

What do you notice?

Can you explain what you have noticed?

*You might like to try Of All the Areas next.*