We consider how measurements of the 21cm radiation from the epoch of reionization (z = 8−12) can constrain the amplitudes of various `shapes' of primordial non-Gaussianity. The limits on these shapes, each parametrized by the non-linear parameter ƒNL, can reveal whether the physics of inflation is more complex than the standard single-field, slow-roll scenario. In this work, we quantify the effects of the well-known local, equilateral, orthogonal and folded types of non-Gaussianities on the 21cm power spectrum, which is expected to be measured by upcoming radio arrays such as the Square-Kilometre Array (SKA). We also assess the prospects of the SKA in constraining these non-Gaussianities, and found constraints that are comparable with those from cosmic-microwave-background experiments such as Planck. We show that the limits on various ƒNL can be tightened to O(1) using a radio array with a futuristic but realistic set of specifications.