It is a classic, with quite a few generalisations. See these links: http://www.artofproblemsolving.com/Forum/viewtopic.php?t=150961 http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10569 http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=217683 http://www.artofproblemsolving.com/Forum/viewtopic.php?f=150&t=237223 http://www.artofproblemsolving.com/Forum/viewtopic.php?f=57&t=241573

We know that using shoelace's theorem, the area will be rational. However, using the formula for the area of the equilateral triangle in terms of side length, we have that the area is irrational. Contradiction. EDIT: This is on the assumption we're on a 2D plane. Are we?

To elaborate on a part of the comment above, the formula is sqrt(3)/4 x s^2. Note that a square of a surd, the side length or the distance between 2 points, is always an integer. The area is irrational, thus contradiction