Summary: We consider an inverse problem of identifying the support \(D\) of a source term in the elliptic equation \[ -\Delta u(x) + q(x)\chi_D(x)u(x) = 0, \quad x\in \Omega, \quad \text{and} \quad u(x) = f(x), \quad x \in \partial\Omega. \] Here \(q\) is a given positive function and \(\chi_D\) is the characteristic function of a subdomain \(D\) such that \(\overline{D} \subset \Omega\). We prove the global uniqueness in this inverse problem within convex hulls of polygons \(D\).