Helli, Wilmer!
A Pythagorean right triangle has integer sides and area. Everybody knows that!
For each of these, two integersided isosceles triangles with integer area exist.
Example: two 345 right triangles can be used to make isosceles triangles
. . 556 and 558.
Is there any reasons why this is not "widely known/quoted"?
Maybe because it is "too obvious"?
. . (Is there such a thing?)
An integersided isosceles triangle (with an even base and integral altitude)
. . can be bisected into two congruent Pythagorean triangles.
Code:
*

**

*  *

*  *

* * * * *
These, in turn, can be assembled into another integersided isosceles triangle.
Code:
*
*  *
*  *
* * * * * * *