Intermediate June 2023 Unit 2 Q18
18. The diagram below shows a semicircle, with radius \(r\), drawn inside a trapezium.
Diagram not drawn to scale
The area of the semicircle is 77 cm\(^2\).
The semicircle touches the line AB.
AB = 22 cm.
Calculate the area of the trapezium ABCD. [5]
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{\pi \times r^2}{2}\) = 77 or equivalent | M1 | Check diagram for answers. |
| \(r^2\) = 49(·0…) or \(r^2 = \dfrac{154}{\pi}\) | m1 | Sight of 49(·0…) implies M1m1. |
| \(r\) = 7(·0…) | A1 | FT ‘their \(r^2\)’ provided M1 awarded. 7 must not be from incorrect working. |
| (Area of trapezium = ) \(\dfrac{2 \times 7(\cdot 0\ldots) + 22}{2} \times 7(\cdot 0\ldots)\) or equivalent | M1 | FT ‘their derived or stated \(r\)’. |
| = 126·0(…)(cm\(^2\)) | A1 | Accept 126·1 or 126 (cm\(^2\)) Mark final answer. |