Robotic manipulation tasks commonly rely on computer vision or tactile sensing to extract the physical characteristics of an object. However, this additional sensing capability adds complexity and financial cost to a robotic system. Our work investigates the inexpensive alternative of feature extraction via proprioceptive sensing. Our goal is to determine whether proprioceptive data combined with in-hand-manipulation provides sufficient information to enable geometric reconstruction of object profiles. We use a newly designed 3-DOF robotic gripper with variable-friction finger surfaces to perform model-free in-hand-manipulation on a set of test objects comprised of two dimensional convex prisms. We have devised a manipulation sequence based on the rotation and sliding of test objects to allow side-counting with the successful measurement of shapes and sizes with average angle and size errors of 1.64% and 6.76% respectively. In addition, we have outlined potential research directions aimed at resolving inherent limitations of proprioceptive approaches and making our algorithm generalisable to any arbitrary shape.