The maximum area is

trivially infinite

if one

simply creates a rectangle three units high and any number of units across (giving it an arbitrarily large area) and fills the first row with red, the second with blue, and the third with yellow.

Note that

any three-in-a-row of the same colour does not count as a triangle (refer to the valid solution of the linked question, which contains many such occurrences).

Previous answer, valid before alteration to question.

The maximum area is

trivially infinite

if one

simply creates a rectangle three units high and any number of units across (giving it an arbitrarily large area) and fills the first row with red, the second with blue, and the third with yellow.

Note that

any three-in-a-row of the same colour does not count as a triangle (refer to the valid solution of the linked question, which contains many such occurrences).

The maximum area is

trivially infinite

if one

simply creates a rectangle one unit high and any number of units across (giving it an arbitrarily large area) and fills it with the three colours in any order.

Note that

any three-in-a-row of the same colour does not count as a triangle (refer to the valid solution of the linked question, which contains many such occurrences).

The maximum area is

trivially infinite

if one

simply creates a rectangle three units high and any number of units across (giving it an arbitrarily large area) and fills the first row with red, the second with blue, and the third with yellow.

Note that

any three-in-a-row of the same colour does not count as a triangle (refer to the valid solution of the linked question, which contains many such occurrences).