Pythagorean Triangles whose Areas are Repdigit Numbers

Theorem
The following Pythagorean triangles have areas consisting of repdigit numbers:

$3-4-5$ Triangle
It has area $6$.

$693-1924-2045$ Triangle
It has area $666 \, 666$.

Proof
From Pythagorean Triangle whose Area is Half Perimeter, the area of the $3-4-5$ triangle is $6$, which is trivially repdigit.

The next Pythagorean triangles in area are:


 * the $6-8-10$ triangle, which has area $\dfrac {6 \times 8} 2 = 24$


 * the $5-2-13$ triangle, which has area $\dfrac {5 \times 12} 2 = 30$

So there are no more Pythagorean triangles whose areas consist of a single digit.

We have that the $693-1924-2045$ triangle is Pythagorean.

Then its area $A$ is given by: