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Isometric Areas

Age 11 to 14 Challenge Level:

Here is an equilateral triangle with sides of length 1.

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

Here are some parallelograms whose side lengths are whole numbers.


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.