Transformation is an art of wavering chattels from one location to the other location or one zone to the other zone or one pattern to the other pattern. Designing any regular or irregular polygonal structures especially in tile pasting plays decisive portrayal of procreation. Tile pasting is a technique of gluing tiles in sequence of specific nature, and subsidize collection of structures to the constructors. The sequence of tile pasting can be analyzed and the best sequential path will be determined using Viterbi Algorithm. The pictorial representation of Viterbi algorithm is the trellis path that hand out more strength to the algorithm which shows the sequential order of tile pasting effectively. This paper will also be initiated to find the renewable energy produced by gluing triangular tiles of different polygonal structures and gives an intention to identify the most effective structure among the shapes discussed.