Sacred Haven of Debauchery

The problem statement does not specify that the triangle is isosceles. Therefore, completely different formulas must be used. Okay, I'll give you a hint. 1/a^2 + 1/b^2 = 1/f^2; c^2 = a^2 + b^2, where a, b are the legs, c is the hypotenuse, and f is the altitude; These need to be combined into a system, and a or b needs to be expressed, which is what I did, and from there, the area can be found using the formula for two legs.

Added 5 minutes later
In general, it's a rather simple problem from the school curriculum. Let's try something from mathematical cybernetics.

Added 7 minutes later
Here's an example:

Does there exist an infinite connected set (in the sense of integer distances) of points in the integer lattice Zn for some n, no three of which lie on the same line?