Higher November 2024 Paper 3 Q13

13 \(ABC\) and \(AED\) are straight lines.
\(BE\) and \(CD\) are parallel.

\(BE = 4.2\) cm
\(CD = 6.3\) cm
\(AC = 10.8\) cm

Work out the area of trapezium \(BCDE\). (3)

Mark scheme

Answer	Mark	Mark scheme
18.9	P1	for using length scale factor to find \(AB\), eg \((AB =)\ 10.8 \div \left(\dfrac{3}{2}\right)\) or \((AB =)\ 10.8 \times \left(\dfrac{2}{3}\right)\ (= 7.2)\) or for using length scale factor to find \(BC\), eg \((BC =)\ 10.8 \div \dfrac{6.3}{6.3 - 4.2}\) or \((BC =)\ 10.8 \times \dfrac{6.3 - 4.2}{6.3}\ (= 3.6)\) or finds area scale factor, eg \(\left(\dfrac{3}{2}\right)^2\) or \(\left(\dfrac{2}{3}\right)^2\)
	P1	for a complete process to find the area of trapezium, eg \(\dfrac{6.3 + 4.2}{2} \times (10.8 - \text{``}7.2\text{''})\) or \(\dfrac{(6.3 - 4.2) \times \text{``}3.6\text{''}}{2} + \text{``}3.6\text{''} \times 4.2\) or \(\dfrac{10.8 \times 6.3}{2} - \dfrac{7.2 \times 4.2}{2}\) or \(\dfrac{10.8 \times 6.3}{2} - \dfrac{10.8 \times 6.3}{2} \div \left(\text{``}\dfrac{3}{2}\text{''}\right)^2\) or \(\dfrac{10.8 \times 6.3}{2} - \dfrac{10.8 \times 6.3}{2} \times \left(\text{``}\dfrac{2}{3}\text{''}\right)^2\)
	A1	accept trailing zeros eg 18.90

Can use a combination of skills but must have a complete process to find \(AB\) or \(BC\) to score this mark