Isometric Areas

We usually use squares to measure area, but what if we use triangles instead?
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You may wish to print off some isometric paper.

Isometric Areas printable sheet
 
 
Here is an equilateral triangle with sides of length 1.

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Isometric Areas
 

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

Here are some parallelograms whose side lengths are whole numbers.

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Isometric Areas
  

Can you find the area, in terms of $T$, of each parallelogram?

Compare the results with the lengths of their edges.

What do you notice?

Can you explain what you've noticed?


Can you find a similar result for trapeziums in which all four lengths are whole numbers?

You might like to try More Isometric Areas next.