Specimen 2020 Paper 1 Q7
7 \(ABCD\) is a rhombus with side length 8 cm
Angle \(ABC = 60^\circ\)
Not drawn accurately
Work out the area of the rhombus.
Give your answer in the form \(a\sqrt{b}\) cm\(^2\) where \(a\) and \(b\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{1}{2} \times 8 \times 8 \times \sin 60\) or \(\dfrac{1}{2} \times 8 \times 8 \times \sin(180 - 60)\) | M1 | oe area of triangle \(ABC\) or area of triangle \(ADC\) |
| \(2 \times\) their area of triangle \(ABC\) or \(2 \times\) their area of triangle \(ADC\) | M1dep | oe fully correct method for area |
| \(32\sqrt{3}\) | A1 | |
| Alternative method 2 | ||
| \(2 \times 8 \times \sin 30\) or \(\sqrt{8^2 + 8^2 - 2 \times 8 \times 8 \times \cos 60}\) or 8 or \(2 \times 8 \times \cos 30\) or \(\sqrt{8^2 + 8^2 - 2 \times 8 \times 8 \times \cos 120}\) or \(8\sqrt{3}\) | M1 | oe diagonal \(AC\) or diagonal \(BD\) |
| \(\dfrac{1}{2} \times\) their \(AC \times\) their \(BD\) | M1dep | oe fully correct method for area |
| \(32\sqrt{3}\) | A1 | |
Additional guidance
| Any fully correct method for the area of the rhombus scores M1M1 eg \(8 \times 8 \times \sin 60\) | M1M1 |