For any m > 0 let Fm = 22m + 1 be the standard Fermat number. It is known that Fm is prime when 0 < m < 4, but these values of m are the only ones for which Fm is known to be prime. By a celebrated theorem of Gauss (see [1]), the prime Fermat numbers are related to the number of sides of regular polygons that can be constructed with ruler and compass. Recall that a Heron triangle is a triangle such that the lengths of its three sides and its area are integers. In this note, we point out a connection between the prime Fermat numbers and the Heron triangles whose sides are prime powers. Our result is the following.