Right angled Triangles will all side integers are called Pythagorean triangles… now using m,n rule

Let the two sides of triangle be m²-n² and 2mn   

Then hypotenuse= m²+n²,  Where m , n are whole numbers

It is easy to see that m = n + 1.

The m,n formula in this case gives

a = m² – n² = (n+1)² – n² = 2 n + 1
b = 2 m n = 2 (n+1) n = 2 n² + 2 n
h = m² + n² = (n+1)² + n² = 2 n² + 2 n + 1

Area of triangle           = ½ a x b

                                    = ½  (2 n + 1)  x  (2 n² + 2 n)

                                    = ½  (2 n + 1)  x  2n (n + 1)

                                    = n (2 n² + 3n + 1)

Which is always divisible by 6