2024 IGCSE Additional Mathematics May/June 0606/12 Q5

DO NOT USE A CALCULATOR IN THIS QUESTION.

In this question, all lengths are in centimetres.

The diagram shows the trapezium \(ABCD\). The lengths of \(AB\), \(BC\) and \(CD\) are \(8\sqrt7-7\), \(\sqrt7+2\) and \(9\sqrt7-9\) respectively. The line \(BC\) is perpendicular to the lines \(AB\) and \(CD\).

1. Find the perimeter of the trapezium, giving your answer in its simplest form.[3]
2. Find the area of the trapezium, giving your answer in the form \(p\sqrt7+q\), where \(p\) and \(q\) are rational numbers.[3]
3. Find \(\cot DBC\), giving your answer in the form \(r\sqrt7+s\), where \(r\) and \(s\) are simplified rational numbers.[3]