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This problem follows on from Isometric Areas.

More Isometric Areas printable sheet
Printable 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?


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