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.