For positive real numbers \(s\), let \(\tau(s)\) denote the set of all obtuse triangles that have area \(s\) and two sides with lengths \(4\) and \(10\). The set of all \(s\) for which \(\tau(s)\) is nonempty, but all triangles in \(\tau(s)\) are congruent, is an interval \([a,b)\). Find \(a^2+b^2\).