0606 P12 - Mar 2021 - Q7 - 9 marks
7924
Do not use a calculator in this question.
The diagram shows a trapezium \(ABCDE\) such that \(AB\) is parallel to \(EC\) and \(ABCD\) is a rectangle. It is given that \(BC=\sqrt{17}+1\), \(ED=\sqrt{17}-1\) and \(DC=\sqrt{17}+4\).
(a) Find the perimeter of the trapezium, giving your answer in the form \(a+b\sqrt{17}\), where \(a\) and \(b\) are integers.
(b) Find the area of the trapezium, giving your answer in the form \(c+d\sqrt{17}\), where \(c\) and \(d\) are integers.
(c) Find \(\tan AED\), giving your answer in the form \(\dfrac{e+f\sqrt{17}}{8}\), where \(e\) and \(f\) are integers.
(d) Hence show that \(\operatorname{sec}^2 AED=\dfrac{81+9\sqrt{17}}{32}\).
