4MA0 Higher June 2017 Paper 4 Q19
19 \(ABCD\) is a kite.
Diagram NOT accurately drawn
Work out the area of the kite.
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
| 0.5 × 6.4 × 9.7 × sin 110 (= 29.16…) | M1 |
| 2 × “29.16…” | M1 |
| 58.3 | A1 |
| (3) | |
| (3 marks) |
Notes
A1: for 58.3 – 58.4
M2 for 6.4 × 9.7 × sin 110
alternative
| Scheme | Marks |
|---|---|
\(AC = \sqrt{6.4^2 + 9.7^2 - 2 \times 9.7 \times 6.4 \times \cos 110}\) (=13.323...) \(DAC = \sin^{-1}\left(\dfrac{\sin 110}{\text{'}13.323\text{'}} \times 9.7\right)\) (= 43.167...) or \(ACD = \sin^{-1}\left(\dfrac{\sin 110}{\text{'}13.323\text{'}} \times 6.4\right)\) (= 26.83...) | M1 |
| Area = (sin ‘43.167..’ × 6.4 × 2 × ‘13.323..’) ÷ 2 Or area = (sin ’26.83..’ × 9.7 × 2 × ‘13.323...’) ÷ 2 | M1 |
| 58.3 | A1 |
Notes
M1: For method to find \(AC\) and angle \(DAC\) or angle \(ACD\)
M1: find \(DB\) and then area using half product of diagonals
A1: for 58.3 – 58.4