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Nano fabrication with biomolecular/DNA self assembly is a promising area of research. Building nano structures with self assembly is both efficient and inexpensive. Soloveichik and Winfree (SIAM J Comput 36(6):1544-1569, ) formalized a two dimensional (2D) tile assembly model based on Wang's tiling technique. Algorithms with an optimal tile complexity of $$\left(\Uptheta\left(\frac{\log(N)}{\log(\log(N))}\right)\right)$$ were proposed earlier to uniquely self assemble an N × N square (with a temperature of α = 2) on this model. However efficient constructions to assemble arbitrary shapes are not known and have remained open. In this paper we present self assembling algorithms to assemble a triangle of base 2 N − 1 (units) and height N with a tile complexity of $$\Uptheta(\log(N)).$$ We also describe how this framework can be used to construct other shapes such as rhombus, hexagon etc. [ABSTRACT FROM AUTHOR]