3.47: Surd trapezium: perimeter, area and cotangent

0606/12/M/J/24 — Question 5 · 9 marks

DO NOT USE A CALCULATOR IN THIS QUESTION.

In this question, all lengths are in centimetres.

The diagram shows trapezium

ABCD

with

AB = 8\sqrt{7} - 7

BC = 2 + \sqrt{7}

and

CD = 9\sqrt{7} - 9

. BC is perpendicular to AB and CD.

(a)

Find the perimeter of the trapezium in its simplest form.

[3]

(b)

Find the area in the form

p + q\sqrt{7}

, where

p

and

q

are rational.

[3]

(c)

Find

\cot\angle DBC

in the form

r + s\sqrt{7}

, where

r

and

s

are simplified rationals.

[3]