Foundation June 2019 Paper 3 Q23
23 The diagram shows a regular hexagon made from six equilateral triangles.
Each side is 10 cm.
The angle ACB is a right angle.
Not to scale
(a) Show that AC = 8.66 cm, correct to 3 significant figures. [4]
(b)
(i) Show that the area of triangle ACB is 21.7 cm2, correct to 3 significant figures. [2]
(ii) Find the area of the hexagon, giving your answer to an appropriate degree of accuracy. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 60 or 30 seen as angle | B1 | May be correctly marked on diagram | Reverse method using 8.66... scores 0 |
| \(10 \times \sin 60\) or \(10 \times \cos 30\) | M2 | M1 for \(\sin 60 = \dfrac{AC}{10}\) oe or \(\cos 30 = \dfrac{AC}{10}\) | |
| 8.660[...] | A1 dep | Dep on at least M1 | |
| Alternative method by Pythagoras | |||
| 5 seen as side | B1 | May be correctly marked on diagram | |
| \(\sqrt{10^2 - 5^2}\) | M2 | or M1 for \(10^2 - 5^2\) | \(10^2\) may be 100 and \(5^2\) may be 25 |
| 8.660[...] | A1 dep | Dep on at least M1 | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(\dfrac{1}{2} \times \dfrac{1}{2} \times 10 \times 8.66[0..]\) oe | M1 | Reverse method using 21.7 scores 0 May be in stages | |
| 21.65[...] | A1 | ||
| (ii) 260 | 2 | M1 for \(12 \times 21.7\) or B1 for 259.8 to 260.4 | Award M1 for alternative complete methods |