Neco 2022 Geography Question 25

A rectangular plateau measures \\(12\\) km by \\(8\\) km. A river enters the plateau at the midpoint of one \\(12\\) km side, flows across the plateau following a sinusoidal path approximated by three half‑waves of the function \\(y = A\sin\left(\frac{\\pi x}{L}\right)\\), where the amplitude \\(A\\) is \\(1\\) km and each half‑wave spans a horizontal length \\(L\\). The river exits at the midpoint of the opposite \\(12\\) km side. Using the approximation that the length of one half‑wave is \\(L\sqrt{1 + \left(\frac{\\pi A}{L}\right)^{2}}\\), determine the approximate total length of the river across the plateau. Give your answer in kilometres to two decimal places.