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# More Isometric Areas

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Matt from Swindon Academy in the UK, Ambrose, Swiss and Piyush from West Island School in Hong Kong and Pete and Neha from International School of Lausanne in Switzerland found a formula for finding the areas of the triangles. Piyush said:

Area of a triangle on isometric paper = Whole number side length $\times$ other whole number side length

Pete and Neha, Matt and Ambrose used parallelograms to explain why this works. This is Ambrose's work:

For every triangle with at least two whole number sides, you can always form a parallelogram by putting 2 triangles together.

Then, from the task, “Isometric Areas”, we know that the area of a parallelogram in “$T$” is $base\times height\times2$.

For the area of a triangle, we can divide this by $2$

So the formula is: $base\times height$.

Matt thought about using small parallelograms, or 'squares', as units:

Swiss also thought about using little parallelograms as 1 unit of area:

To find the area of a normal triangle, the formula is b $\times$ h $\div$ 2 but since we're trying to find number of Triangles, you don't need to divide by 2 because 2$T$=1 unit of area.

Area of a triangle on isometric paper = Whole number side length $\times$ other whole number side length

Pete and Neha, Matt and Ambrose used parallelograms to explain why this works. This is Ambrose's work:

For every triangle with at least two whole number sides, you can always form a parallelogram by putting 2 triangles together.

Then, from the task, “Isometric Areas”, we know that the area of a parallelogram in “$T$” is $base\times height\times2$.

For the area of a triangle, we can divide this by $2$

So the formula is: $base\times height$.

Matt thought about using small parallelograms, or 'squares', as units:

Swiss also thought about using little parallelograms as 1 unit of area:

To find the area of a normal triangle, the formula is b $\times$ h $\div$ 2 but since we're trying to find number of Triangles, you don't need to divide by 2 because 2$T$=1 unit of area.

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?