2026 CSS P1 Q7

Do not use a calculator for this question.

The diagram shows a trapezium \(ABCD\), \(AB\) and \(CD\) are parallel sides. The length of \(AB\) is \((6+\sqrt3)\) cm.

The perpendicular height of the trapezium is \((4-\sqrt3)\) cm and the area of the trapezium is 52 cm\(^2\). Find the exact length of \(l\), which is the length of \(CD\) in the form of \((a+b\sqrt3)\) cm, where \(a\) and \(b\) are integers.[7]