(CIE 0606/2021 March/12/Q7)
7DO NOT USE A CALCULATOR IN THIS QUESTION
In this question all lengths are in centimetres.
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. [3]
(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. [2]
(d) Hence show that $\sec^2 AED = \dfrac{81+9\sqrt{17}}{32}.$ [2]
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