Foundation June 2025 Paper 1 Q26

Diagram NOT accurately drawn

\(ABCD\) is a trapezium with one line of symmetry.

angle \(ADC = 60^\circ\) \(AD = 12\) cm \(DC = 47\) cm

Work out the area of the trapezium.
Give your answer correct to 3 significant figures.
Show your working clearly.

(5)

Mark scheme

Scheme	Marks
eg \(12\sin 60\left(= 6\sqrt{3} = 10.3(9\ldots)\right)\) or \(\sqrt{12^2 - \text{``}{6}\text{''}^2}\left(= 6\sqrt{3} = 10.3(9\ldots)\right)\) or (Area \(ADC\) =) \(\dfrac{1}{2} \times 12 \times 47 \times \sin 60 \;(= 244.2\ldots)\)	M1
eg \(12\cos 60 (= 6)\) or \(\sqrt{12^2 - \left(\text{``}{6\sqrt{3}}\text{''}\right)^2}\;(= 6)\)	M1
eg (\(AB\) =) 47 – “6” – “6” (= 35)	M1
eg (Trapezium =) \(\dfrac{1}{2} \times \left(47 + \text{``}{35}\text{''}\right) \times \text{``}{10.3(9\ldots)}\text{''}\) or (Rectangle + 2 × Triangle =) \(\text{``}{35}\text{''} \times \text{``}{10.3(9\ldots)}\text{''} + 2 \times \dfrac{1}{2} \times \text{``}{6}\text{''} \times \text{``}{10.3(9\ldots)}\text{''}\) or (Rectangle + 2 × Triangle =) \(\text{``}{35}\text{''} \times \text{``}{10.3(9\ldots)}\text{''} + 2 \times \dfrac{1}{2} \times \text{``}{6}\text{''} \times 12 \times \sin 60\) or (Triangle \(ADC\) + Triangle \(ABC\) =) \(\text{``}{244.2\ldots}\text{''} + \dfrac{1}{2} \times 12 \times \text{``}{35}\text{''} \times \sin 120\) oe eg \(\left(47 - \text{``}{6}\text{''}\right) \times \text{``}{10.3(9\ldots)}\text{''}\)	M1
Working required Answer: 426	A1
	(5)
	(5 marks)

M1: for a method find the height of the trapezium
or the area of triangle \(ADC\)

The first two M1 marks can be awarded in either order

M1: (indep)

for a method find the base of the triangle, condone missing brackets around \(\text{``}{6\sqrt{3}}\text{''}\)

The first two M1 marks can be awarded in either order

M1: (dep on previous M1)
for method to find the length of \(AB\)

M1: for a complete method

There are other methods and marks should be awarded for a complete method that should give the correct area

A1: (dep on M1) allow 420 – 427 from correct working