The objectives of radiotherapy treatment is to kill cancerous cells while minimizing damage to surrounding healthy tissues. The tumour location uncertainty "forces" oncologists to prescribe a larger treatment area than required in order to ensure that the whole tumour is receiving the prescribed dose. The problem is more acute when a tumour can move during treatment, e.g., as a result of breathing. In this paper, we present an algorithm for computing the area covered by a tumor as a result of a cyclic motion during treatment. Our algorithm solves the following geometric problem: Given an n-vertices convex polygon P = {v₁, v₂, . . . , v_n}, a monotone chain C = {c₁, c₂, . . . , c_m}, compute a minimums area polygon Q that includes all the space covered by P as it is translated along C such that v₁ ∊? P touches C. Here, we present a simple algorithm when P is a convex polygon. Our algorithm takes O(mn + m log n log(m + n)) time in the worst case.