Foundation June 2024 Paper 2R Q26
26 The diagram shows a hexagon \(ABCDEF\)

Diagram NOT accurately drawn
Angle \(BCF = 30°\)
\(AB\), \(FC\) and \(ED\) are parallel.
Calculate the area of \(ABCDEF\)
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| \(23 \times 4.7\) (= 108.1) oe | B1 |
\(\sin 30 = \dfrac{(x)}{5}\) or \(\dfrac{(x)}{\sin 30} = \dfrac{5}{\sin 90}\) oe where \(x\) = height of trapezium or \(5\cos30\) \(\left(= \dfrac{5\sqrt3}{2} = 4.33...\right)\) and (\(x^2 =\)) \(5^2 - \text{``}{5\cos30}\text{''}^2\) (= 6.25) | M1 |
(\(x =\)) \(5 \sin 30\) (= 2.5) oe or (\(x =\)) \(\dfrac{5}{\sin 90} \times \sin 30\) (= 2.5) oe or (\(x =\)) \(\sqrt{5^2 - \text{``}{5\cos30}\text{''}^2}\) (= 2.5) | M1 |
\(\tfrac12\times(11+23)\times\text{``}{2.5}\text{''}\) (= 42.5) oe or \(\left(\tfrac12\times\text{``}{2.5}\text{''}\times(23-11)\right) + (11\times\text{``}{2.5}\text{''})\) (= 42.5) oe or \(\left(\tfrac12\times\text{``}{2.5}\text{''}\times(23-11-\text{``}{4.3}\text{''})\right) + (11\times\text{``}{2.5}\text{''}) + \left(\tfrac12\times\text{``}{2.5}\text{''}\times\text{``}{4.3}\text{''}\right)\) (= 42.5) oe or \((11\times\text{``}{2.5}\text{''}) + \left(\tfrac12\times5\times(23-11)\times\sin 30\right)\) (= 42.5) oe or \((23\times\text{``}{2.5}\text{''}) - \left(\tfrac12\times\text{``}{2.5}\text{''}\times(23-11-\text{``}{4.3}\text{''})\right) - \left(\tfrac12\times\text{``}{2.5}\text{''}\times\text{``}{4.3}\text{''}\right)\) (= 42.5) oe or \((23\times(\text{``}{2.5}\text{''}+4.7)) - \left(\tfrac12\times\text{``}{2.5}\text{''}\times(23-11-\text{``}{4.3}\text{''})\right) - \left(\tfrac12\times\text{``}{2.5}\text{''}\times\text{``}{4.3}\text{''}\right)\) oe | M1 |
| Working required Answer: 150.6 | A1 |
| (5) | |
| (5 marks) |
Notes
B1: (indep) May be embedded in \(23 \times (4.7 + 2.5)\) (= 165.6)
M1: for a correct method to find the area of the trapezium or the whole shape
A1: dep on M1
awrt 150.6
Allow 151
Accept \(\dfrac{753}{5}\)