More Isometric Areas

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

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 $1T$.

Image
More Isometric Areas
 

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 $4$.

Image
More Isometric Areas
 

 

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.