2024 CCHY P1 Q2

A triangle has a base of \(\left(\frac{1}{\sqrt{2}} - \frac{\sqrt{32}}{2} + \frac{16}{\sqrt{48}}\right)\) m and a height of \(h\) m. Given that the area of the triangle is \(\left(2\sqrt{2} - \sqrt{3}\right)\) m\(^2\), find, without using calculator, the value of \(h\) in the form \(\frac{a\sqrt{6} + b}{5}\) where \(a\) and \(b\) are integers.[5]