2D Area & Perimeter: WJEC GCSE Intermediate June 2025 Unit 1 Q9

Intermediate June 2025 Unit 1 Q9

WJECIntermediateCurrent spec7 marks2D Area & Perimeter

9. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram below shows a trapezium, ABCD.

Trapezium ABCD with AB parallel to DC; AE perpendicular to DC with E on DC

Diagram not drawn to scale

The area of the right-angled triangle, AED, is 24 cm\(^2\).
The length of AB is 3 cm.
The length of DE is 4 cm.
The length of EC is 10 cm.

Calculate the area of the trapezium, ABCD.
You must show all your working. [5 + 2 OCW]

From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)

Trapezium ABCD outlined, with AB 3 cm, AE 12 cm and DC 14 cm marked — Mark scheme

Triangle AED 24 cm² and trapezium ABCE 78 cm² (AE 12 cm, EC 10 cm) — Mark scheme

Scheme	Marks	Comments
(AE = ) 2 × 24 ÷ 4 or equivalent	M2	Check diagram. May be seen in stages. Award M1 for 24 = ½ × 4 × AE or equivalent.
(AE = ) 12 (cm)	A1	Award M2 A1 for unsupported or embedded 12 (cm). May be implied in later working.
An appropriate valid method for calculating the area of trapezium ABCD or the area of trapezium ABCE For example: \[\dfrac{(3 + 10 + 4) \times 12}{2}\] \[(24\ +)\ \dfrac{(3 + 10) \times 12}{2}\] \[(24\ +)\ 12 \times 3 + \dfrac{(10 - 3) \times 12}{2}\] \[\dfrac{(3 + 4 + 3) \times 12}{2} + \dfrac{(10 - 3) \times 12}{2}\] \[(24\ +)\ 12 \times 3 + 12 \times (10 - 3) - \dfrac{(10 - 3) \times 12}{2}\] \[(24\ +)\ 10 \times 12 - \dfrac{(10 - 3) \times 12}{2}\] \[\dfrac{(3 + 4 + 3) \times 12}{2} + 12 \times (10 - 3) - \dfrac{(10 - 3) \times 12}{2}\] \[(4 + 10) \times 12 - \dfrac{(10 - 3) \times 12}{2} - \dfrac{12 \times 4}{2}\]	M1	FT ‘their derived or stated 12’. Allow 4·9 ≤ ‘their 12’ ≤ 5·3 (measured height). Award M1 for complete method or intention of complete method using brackets provided not contradicted e.g. 3 + (10 + 4) × 12 ÷ 2 = 87 M0 A0. Note:
= 102 (cm²)	A1	Must be for an area of ABCD.
Organisation and Communication.	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means.
Accuracy of writing.	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.

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