In the present paper previously established results on the area of equilateral triangles with side length 1 in Banach-Minkowski planes [H. Reimann, Wiss. Z. PH Erfurt/Mühlhausen 23, No. 1, 124-132 (1987; Zbl 0627.52006) and M. Wellmann and the author, Wiss. Z. PH Erfurt/Mühlhausen 27, No. 1, 21-28 (1991; Zbl 0753.52001)] are transferred to obtain theorems on the area of Releaux triangles with width 1. For example, the Minkowski area of such a Releaux triangle always lies in the interval \([\pi/6, \pi/4]\). It is equal to \(\pi/6\) if and only if the gauge figure (indicatrix) is an affinely regular hexagon. It is equal to \(\pi/4\) if and only if the gauge figure is a parallelogram. In addition it turns out that the gauge figure is completely determined by one Releaux triangle.
For the entire collection see [Zbl 0809.00022].