4MA0 Higher June 2013 Paper 4R Q22
22
Diagram NOT accurately drawn
The diagram shows a regular hexagon.
The perimeter of the hexagon is 42 cm.
Calculate the area of the hexagon.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{42}{6}\) or 7 | B1 |
\(\dfrac{1}{2} \times 7^2 \times \sin 60^\circ\) or 21.2(1... Or \(7 \times \sqrt{14^2 - 7^2}\) and \(\dfrac{1}{2} \times 7 \times \sqrt{14^2 - 7^2}\) | M2 |
| “21.21...” × 6 or 7ד12.12” + 2ד21.21” | M1 |
| 127 | A1 |
| (5) |
Notes
M2: Alternative methods
M1 for \(\sqrt{7^2 - 3.5^2}\) or \(7 \sin 60^\circ\) or 6.062...
M1 (dep) for \(\dfrac{1}{2} \times 7 \times \text{“}6.062...\text{”}\) or 21.21...
Or
M1 for \(\sqrt{14^2 - 7^2}\) and 3.5
M1 for \(7 \times \text{“}12.12\text{”}\) and \(\dfrac{1}{2} \times 3.5 \times \text{“}12.12...\text{”}\)
Or
Other equivalent methods.
M1: dep on preceding 3 marks summing all the areas to make up the hexagon
A1: for answer rounding to 127
Alternatives for Question 22
(The symbols garbled in the printed middle boxes read \(\tfrac{1}{2}(7 + 14) \times \dfrac{7\sqrt{3}}{2}\).)