Weisstein states "The smallest known area shared by three primitive right triangles is 13123110, corresponding to the triples (4485, 5852, 7373), (1380, 19019, 19069), and (3059, 8580, 9109) (Beiler 1966, p. 127; Gardner 1984, p. 160), as discovered by C. L. Shedd in 1945."

Devlin has "given a positive whole number d. Is there a right triangle whose sides are rational numbers (i.e., whole numbers or fractions) for which the area is exactly d?" He answers with (3, 4, 5) corresponding to d = 6 and (3/2, 20/3, 41/6) of d = 5. Moreover, he states that "there is a right triangle with rational sides having an area d if and only if the equation

y² = x³ - d²x

has rational solutions for x and y with y" not zero.

Many web urls discuss this in detail. exposition References

Eric W. Weisstein, World of Mathematics, 1999, CRC Press LLC.

Devlin, Keith The Millennium Problems, NY: Basic Books, 2002.