Geometric optimisation with a trigonometric model

A composite region contains a fixed rectangle of area \(3\,\mathrm{square\ units}\) and an attached triangular section

The triangular sides are \(6\sin(u)\,\mathrm{units}\) and \(4\cos(u)\,\mathrm{units}\)

The controlling angle is \(u\), where \(u=x\). The variable angle \(x\) lies in \(x\in\left[0,\frac{1}{2}\pi\right]\). All angles are measured in radians

Write the total area model from the geometric data, then enter its coefficients