We report on the observation of terahertz transparency in random arrays of the single rectangular holes and slits with the areal coverage of only 12%. The terahertz transparency occurs at the fundamental shape resonance of the rectangular holes and confirms the theoretical predictions of earlier works of Garcia-Vidal et al. [Phys. Rev. Lett. 95, 103901 (2005)] on single rectangular holes and of Ruan and Qiu [Phys. Rev. Lett. 96, 233901 (2006)] on random arrays of holes.