It seems you are
A rectangle triangle (a triangle with a right angle)
I'm a friend of Pythagoras,
well more like a son of Pythagoras.
Pythagoras is the author of the theorem named after him, applicable on rectangle triangles.
I am field,
not a baseball field.
But a field of mats.
A triangle is a polygon, it has an area, a perimeter... It occupies space.
My mum's name is atwo,
My dad's name is btwo,
Together, they made me- ctwo.
This refers to Pythagora's theorem $a^2 + b^2 = c^2$. The square of the length of the hypotenuse is equal to the sum of the square of the length of the two ther sides.
My leg is always shorter than my arms combined,
Sure, my leg can be a hypocrite,
Or something along those lines.
The triangle's "leg", its hypotenuse, is always shorter than the combined lengths of the two other sides (arms). Hypotenuse also starts a bit like the word hypocrite.
Well, anyway I better get going,
But I hope you'll get to know me,
Since i'm quite popular, really.
One would learn about this concept in school, and use it a lot throughout their scholarship.