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More Isometric Areas

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
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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?


You might like to try Of All the Areas next.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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