A spectral triple is an object which is described using an algebra of operators on a Hilbert space and an unbounded self-adjoint operator, called a Dirac operator. This model may be applied to the study of classical geometrical objects .The article contains a construction of a spectral triple associated to some classical fractal subsets of the plane, and it is demonstrated that you can read of many classical geometrical structures, such as distance, measure and Hausdorff dimension from the spectral triple.