Higher November 2021 Paper 2 Q18
18 Here is a quadrilateral \(ABCD\).
Diagram NOT accurately drawn
Calculate the area of quadrilateral \(ABCD\).
Give your answer correct to 3 significant figures.
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| \((AC^2 =)\ 9^2 + 12^2 - 2 \times 9 \times 12 \times \cos 60\ (= 117)\) or \((AC^2 =)\ 81 + 144 - 108\ (= 117)\) oe | M1 |
| \((AC =)\ \sqrt{117}\) or \(3\sqrt{13}\) or 10.8(16653…) | A1 |
| (area \(ABC\) =) \(0.5 \times 9 \times 12 \times \sin 60\ (= 27\sqrt{3}\) or 46.7(653….)) | M1 |
| (area \(ACD\) =) \(0.5 \times 7 \times \text{‘}{\sqrt{117}}\text{’} \times \sin 84\) (=37.6(50896…)) | M1 |
| Working required Answer: 84.4 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: oe eg
\(BM = 9\cos 60\ (= 4.5)\) and \(AM = 9\sin 60\ \left(= \dfrac{9\sqrt{3}}{2}\right)\) and
\(AC^2 = \left(\text{‘}{\dfrac{9\sqrt{3}}{2}}\text{’}\right)^2 + (12 - \text{‘}{4.5}\text{’})^2\)
(where AM is perpendicular to BC)
A1: oe
M1: indep or \(\dfrac{1}{2} \times \text{‘}{\dfrac{9\sqrt{3}}{2}}\text{’} \times 12\ (= 27\sqrt{3})\) oe
M1: dep on 1st M1
A1: dep on M3 awrt 84.4