Tensegrity structures show great potential in large scale space structure applications. Comprised of struts suspended in a network of pre-tensioned cables, tensegrities offer lower mass than their truss alternatives, with good potential for shape-changing applications by adjusting member lengths. This research offers a form-finding approach with a focus on maintaining geometric descriptions of member length components while enforcing equilibrium requirements. In doing so, the end results describe all equilibrated shapes a particular tensegrity may achieve in terms of member length components, thus compactly characterizing the range of achievable shapes for a particular connectivity. Describing the range of achievable shapes this way shows great promise for use in designing tensegrities for shape-changing applications. A triplex tensegrity is used to demonstrate the utility of these results in shape selection for morphing applications, with particular emphasis on a module-based area-spanning tensegrity as the backbone for a paraboloid reflector.