### Abstract.

The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 5] were expressed by Müller, under the one-parameter closed planar motions in the complex sense. Also, Müller had given Holditch theorem in the complex sense, [6].

In this paper, in analogy with Complex motions as given by Müller [6], the Steiner formula and the mixture area formula are obtained under one parameter hyperbolic motions. Also Holditch theorem was expressed in the hyperbolic sense.