Foundation June 2019 Paper 1 Q23
23 The diagram shows a shape made from a right-angled triangle and a semicircle.
Diagram NOT accurately drawn
\(AC\) is the diameter of the semicircle.
\(BA = BC = 6\) cm
Angle \(ABC = 90^\circ\)
Work out the area of the shape.
Give your answer correct to 1 decimal place.
(5)
| Scheme | Marks |
|---|---|
| 0.5 × 6 × 6 (=18) | M1 |
| (\(d^2\) =) \(6^2 + 6^2\) (=72) or \(\dfrac{AC}{(\sin 90)} = \dfrac{6}{\sin 45}\) | M1 |
| \(\sqrt{6^2 + 6^2}\) (\(= \sqrt{72} = 6\sqrt{2}\) =8.4(85…)or 8.5) or (\(AC = \dfrac{6(\sin 90)}{\sin 45} = 6\sqrt{2}\) =8.4(85…)or 8.5) oe | M1 |
| \(0.5 \times \pi \times \left(\dfrac{\text{"8.48.."}}{2}\right)^2\) (= 9\(\pi\) or 28….) | M1 |
| 46.3 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: For area of triangle, or may use \(\dfrac{1}{2} \times 6 \times 6\sqrt{2}\sin 45\) or \(\dfrac{1}{2} \times 6\sqrt{2} \times 3\sqrt{2}\) oe
A1: for 46.2 – 46.3